1. Question 1 of 120

   The sum of angles around a point is:

   A 90° B 360° C 180° D 270°
2. Question 2 of 120

   The circumference of a circle is 88 cm (use π = 22/7). Find its radius.

   A 7 cm B 14 cm C 11 cm D 22 cm
3. Question 3 of 120

   A triangle with one interior angle greater than 90° is called:

   A An acute triangle B An obtuse triangle C A right triangle D An equilateral triangle
4. Question 4 of 120

   In an equilateral triangle, the centroid, orthocenter, circumcenter, and incenter:

   A Are always four distinct points B All coincide at a single point C Lie on a straight line but are distinct D Cannot be determined
5. Question 5 of 120

   Two complementary angles differ by 20°. Find the smaller angle.

   A 25° B 35° C 30° D 40°
6. Question 6 of 120

   Find the perimeter of an equilateral triangle with side length 7 cm.

   A 14 cm B 18 cm C 21 cm D 28 cm
7. Question 7 of 120

   A tangent to a circle is always _____ to the radius drawn at the point of contact.

   A Perpendicular B Parallel C Equal in length D At a 45° angle
8. Question 8 of 120

   The sum of the interior angles of a quadrilateral is:

   A 360° B 180° C 270° D 540°
9. Question 9 of 120

   The area of an equilateral triangle with side length a is given by:

   A (√3/4)a² B a²/2 C (√3/2)a² D √3 × a²
10. Question 10 of 120

    The angle formed between a radius and a tangent line at the point where the tangent touches the circle is:

    A 45° B 60° C It varies depending on the circle's size D 90°
11. Question 11 of 120

    The centroid of a triangle divides each median from the vertex in the ratio:

    A 2 : 1 B 1 : 1 C 1 : 2 D 3 : 1
12. Question 12 of 120

    Two similar triangles have corresponding sides in the ratio 1:2. Find the ratio of their areas.

    A 1:4 B 1:2 C 1:3 D 1:8
13. Question 13 of 120

    The area of a semicircle with radius r is given by:

    A πr² B 2πr² C ½πr² D ¼πr²
14. Question 14 of 120

    When two straight lines intersect, the vertically opposite angles formed are:

    A Equal B Complementary C Supplementary D Always 90° each
15. Question 15 of 120

    The angle subtended by an arc at the center of a circle is related to the angle subtended by the same arc at the circumference by which rule?

    A The central angle is twice the inscribed (circumference) angle B They are always equal C The inscribed angle is twice the central angle D They are always supplementary
16. Question 16 of 120

    Angles inscribed in the same segment of a circle, subtending the same arc, are always:

    A Equal B Supplementary C Complementary D Twice each other
17. Question 17 of 120

    An inscribed angle in a circle measures 40°. Find the central angle subtending the same arc.

    A 20° B 80° C 40° D 160°
18. Question 18 of 120

    A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

    A 6 B 7 C 12 D 5
19. Question 19 of 120

    If each interior angle of a regular polygon is 150°, how many sides does it have?

    A 10 B 11 C 12 D 15
20. Question 20 of 120

    Equal chords of a circle are always:

    A Parallel to each other B Perpendicular to each other C Tangent to each other D Equidistant from the center
21. Question 21 of 120

    Two tangents drawn to a circle from the same external point are:

    A Never equal B Equal in length C Perpendicular to each other always D Parallel to each other
22. Question 22 of 120

    A line segment joining two points on a circle is called a:

    A Radius B Chord C Diameter D Tangent
23. Question 23 of 120

    According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be:

    A Equal to the third side B Greater than the third side C Less than the third side D Twice the third side
24. Question 24 of 120

    In similar triangles, the ratio of their perimeters equals:

    A The square of the ratio of corresponding sides B The ratio of their areas C The ratio of corresponding sides D It cannot be determined
25. Question 25 of 120

    Two angles are supplementary, and one is 3 times the other. Find the larger angle.

    A 135° B 45° C 90° D 120°
26. Question 26 of 120

    A triangle with all three sides of different lengths is called:

    A Equilateral B Isosceles C Scalene D Right-angled
27. Question 27 of 120

    In similar triangles, corresponding sides are always:

    A Equal B Perpendicular C Parallel D Proportional
28. Question 28 of 120

    Circles that share the same center but have different radii are called:

    A Congruent circles B Tangential circles C Concentric circles D Intersecting circles
29. Question 29 of 120

    An isosceles right triangle has angles of:

    A 30°, 60°, 90° B 60°, 60°, 60° C 40°, 50°, 90° D 45°, 45°, 90°
30. Question 30 of 120

    The circumference of a circle is given by the formula:

    A πr² B 2πr C πd² D πr
31. Question 31 of 120

    Find the circumference of a circle with radius 7 cm (use π = 22/7).

    A 22 cm B 88 cm C 154 cm D 44 cm
32. Question 32 of 120

    A central angle in a circle measures 100°. Find the inscribed angle subtending the same arc.

    A 25° B 100° C 50° D 200°
33. Question 33 of 120

    The region of a circle bounded by two radii and the arc between them is called a:

    A Sector B Segment C Chord region D Tangent region
34. Question 34 of 120

    When two parallel lines are cut by a transversal, the alternate interior angles are:

    A Supplementary B Complementary C Equal D Vertically opposite
35. Question 35 of 120

    The area of a triangle is given by the formula:

    A base × height B base + height C ½ × base × height D 2 × base × height
36. Question 36 of 120

    In a cyclic quadrilateral, opposite angles are always:

    A Equal B Supplementary C Complementary D Twice each other
37. Question 37 of 120

    According to the Pythagorean theorem, for a right triangle with legs a, b and hypotenuse c:

    A a + b = c B a² - b² = c² C a² + b² = c² D a × b = c²
38. Question 38 of 120

    From an external point, how many tangents can be drawn to a given circle?

    A Exactly two B Exactly one C Exactly three D Infinitely many
39. Question 39 of 120

    Which congruence criterion states that two triangles are congruent if two angles and the included side are equal?

    A ASA B SSS C SAS D RHS
40. Question 40 of 120

    The point of intersection of the angle bisectors of a triangle is called the:

    A Incenter B Centroid C Orthocenter D Circumcenter
41. Question 41 of 120

    Which congruence criterion applies specifically to right triangles, comparing the hypotenuse and one side?

    A SSS B RHS C SAS D ASA
42. Question 42 of 120

    Can sides of length 5, 6, and 10 form a triangle?

    A Yes, since 5+6 = 11 is greater than 10 B No, since 5+6 = 11 is greater than 10 C No such triangle can exist with these values D Cannot be determined without angles
43. Question 43 of 120

    When two parallel lines are cut by a transversal, the co-interior (allied/consecutive interior) angles are:

    A Supplementary B Equal C Complementary D Vertically opposite
44. Question 44 of 120

    The sum of the exterior angles of any convex polygon, taken one at each vertex, is always:

    A 180° B 360° C 270° D Depends on the number of sides
45. Question 45 of 120

    Find the area of a semicircle with radius 7 cm (use π = 22/7).

    A 44 cm² B 154 cm² C 22 cm² D 77 cm²
46. Question 46 of 120

    Which congruence criterion states that two triangles are congruent if all three corresponding sides are equal?

    A SAS B ASA C SSS D RHS
47. Question 47 of 120

    The area of a circle is given by the formula:

    A 2πr B 2πr² C πr² D πd
48. Question 48 of 120

    The sum of the interior angles of a pentagon (5 sides) is:

    A 360° B 540° C 450° D 630°
49. Question 49 of 120

    In an isosceles triangle, which pair of angles is always equal?

    A All three angles B The two base angles (opposite the equal sides) C No angles are necessarily equal D Only the exterior angles
50. Question 50 of 120

    From a point lying exactly on a circle, how many tangents can be drawn to that circle?

    A Zero B Exactly one C Exactly two D Infinitely many
51. Question 51 of 120

    The region of a circle bounded by a chord and the arc it cuts off is called a:

    A Sector B Semicircle C Annulus D Segment
52. Question 52 of 120

    If the diameter of a circle is 20 cm, find its radius.

    A 10 cm B 5 cm C 20 cm D 40 cm
53. Question 53 of 120

    A triangle with exactly two equal sides is called:

    A Equilateral B Scalene C Obtuse D Isosceles
54. Question 54 of 120

    Using Heron's Formula, find the area of a triangle with sides 3, 4, and 5.

    A 4 B 5 C 7 D 6
55. Question 55 of 120

    The Midsegment Theorem states that a segment joining the midpoints of two sides of a triangle is:

    A Perpendicular to the third side and equal to it in length B Parallel to the third side and half its length C Equal in length to the third side D Twice the length of the third side
56. Question 56 of 120

    In a 30°-60°-90° triangle, the sides are in the ratio:

    A 1 : √3 : 2 B 1 : 1 : √2 C 3 : 4 : 5 D 1 : 2 : 3
57. Question 57 of 120

    An angle that measures between 180° and 360° is called:

    A An obtuse angle B A straight angle C An acute angle D A reflex angle
58. Question 58 of 120

    A triangle has two interior angles of 50° and 60°. Find the exterior angle at the third vertex.

    A 70° B 100° C 110° D 120°
59. Question 59 of 120

    Find the length of an arc subtending a 90° angle at the center of a circle with radius 14 cm (use π = 22/7).

    A 11 cm B 44 cm C 22 cm D 88 cm
60. Question 60 of 120

    The formula for the length of an arc subtending an angle θ at the center of a circle of radius r is:

    A (θ/360) × πr² B (θ/360) × 2πr C (θ/180) × πr D θ × 2πr
61. Question 61 of 120

    Find the area of an equilateral triangle with side length 4 cm.

    A 2√3 cm² B 4√3 cm² C 8√3 cm² D 16√3 cm²
62. Question 62 of 120

    A triangle has two angles of 40° and 70°. Find the third angle.

    A 70° B 60° C 80° D 90°
63. Question 63 of 120

    An angle bisector divides an angle into:

    A Two unequal parts B Two equal parts C Three equal parts D Four equal parts
64. Question 64 of 120

    When two parallel lines are cut by a transversal, the corresponding angles are:

    A Supplementary B Equal C Complementary D Always 90°
65. Question 65 of 120

    A perpendicular drawn from the center of a circle to a chord always:

    A Is equal to the chord's length B Passes through another point on the circle only C Bisects the chord D Has no fixed relationship with the chord
66. Question 66 of 120

    An 80° angle is bisected. Find the measure of each resulting angle.

    A 20° B 40° C 30° D 45°
67. Question 67 of 120

    Can sides of length 3, 4, and 8 form a triangle?

    A Yes, since 3+4 = 7 is close to 8 B Yes, all triangles are possible C Cannot be determined D No, since 3+4 = 7 is less than 8
68. Question 68 of 120

    In an equilateral triangle, each interior angle measures:

    A 60° B 45° C 90° D 120°
69. Question 69 of 120

    The angles of a triangle are in the ratio x : 2x : 3x. Find the largest angle.

    A 90° B 30° C 60° D 120°
70. Question 70 of 120

    In a 30°-60°-90° triangle, if the side opposite the 30° angle is 5, find the hypotenuse.

    A 5 B 10 C 5√3 D 10√3
71. Question 71 of 120

    A triangle with all interior angles less than 90° is called:

    A An obtuse triangle B A right triangle C An acute triangle D A scalene triangle (necessarily)
72. Question 72 of 120

    When two parallel lines are cut by a transversal, the alternate exterior angles are:

    A Supplementary B Complementary C Always right angles D Equal
73. Question 73 of 120

    Two triangles are similar if:

    A They have exactly the same size and shape B Only one pair of sides is equal C Two of their corresponding angles are equal (AA similarity) D They have the same perimeter
74. Question 74 of 120

    The sum of the interior angles of a hexagon (6 sides) is:

    A 540° B 630° C 720° D 900°
75. Question 75 of 120

    Find the supplement of a 65° angle.

    A 105° B 125° C 135° D 115°
76. Question 76 of 120

    Two angles whose sum is 90° are called:

    A Supplementary angles B Vertical angles C Complementary angles D Adjacent angles
77. Question 77 of 120

    Two straight lines intersect, forming four angles. If one angle is 70°, find its adjacent (supplementary) angle.

    A 70° B 90° C 110° D 120°
78. Question 78 of 120

    Find the complement of a 35° angle.

    A 45° B 65° C 55° D 145°
79. Question 79 of 120

    Two adjacent angles whose non-common sides form a straight line are called a:

    A Vertical pair B Complementary pair C Corresponding pair D Linear pair
80. Question 80 of 120

    Which congruence criterion states that two triangles are congruent if two sides and the included angle are equal?

    A SSS B ASA C AAS D SAS
81. Question 81 of 120

    A line that touches a circle at exactly one point is called a:

    A Chord B Secant C Diameter D Tangent
82. Question 82 of 120

    If two sides of a triangle are 6 cm and 9 cm, which of the following CANNOT be the length of the third side?

    A 4 cm B 10 cm C 14 cm D 15 cm
83. Question 83 of 120

    In a cyclic quadrilateral, one angle measures 85°. Find its opposite angle.

    A 85° B 90° C 105° D 95°
84. Question 84 of 120

    An angle that measures between 90° and 180° is called:

    A An acute angle B A reflex angle C An obtuse angle D A straight angle
85. Question 85 of 120

    An angle that measures less than 90° is called:

    A An obtuse angle B An acute angle C A reflex angle D A right angle
86. Question 86 of 120

    A midsegment of a triangle measures 6 cm. Find the length of the corresponding third side.

    A 3 cm B 6 cm C 12 cm D 9 cm
87. Question 87 of 120

    A right triangle has a hypotenuse of 10 and one leg of 6. Find the other leg.

    A 6 B 8 C 7 D 9
88. Question 88 of 120

    Find the area of a right triangle with legs of length 5 cm and 12 cm.

    A 17 cm² B 60 cm² C 30 cm² D 65 cm²
89. Question 89 of 120

    The angle inscribed in a semicircle is always:

    A 45° B 60° C 180° D 90°
90. Question 90 of 120

    The point of intersection of the perpendicular bisectors of the sides of a triangle is called the:

    A Orthocenter B Incenter C Centroid D Circumcenter
91. Question 91 of 120

    A perpendicular drawn from a vertex of a triangle to the opposite side (or its extension) is called a(n):

    A Median B Altitude C Angle bisector D Perpendicular bisector
92. Question 92 of 120

    A right triangle has a hypotenuse of 13 and one leg of 5. Find the other leg.

    A 12 B 8 C 10 D 14
93. Question 93 of 120

    Each exterior angle of a regular octagon (8 sides) measures:

    A 45° B 30° C 36° D 60°
94. Question 94 of 120

    The longest possible chord of a circle is:

    A The radius B Any arbitrary chord C The diameter D The tangent
95. Question 95 of 120

    The sum of angles on a straight line is:

    A 180° B 90° C 270° D 360°
96. Question 96 of 120

    The exterior angle of a triangle is equal to:

    A The adjacent interior angle B Half the sum of all interior angles C 180° minus the largest interior angle D The sum of the two remote (non-adjacent) interior angles
97. Question 97 of 120

    A line segment joining a vertex of a triangle to the midpoint of the opposite side is called a:

    A Altitude B Perpendicular bisector C Angle bisector D Median
98. Question 98 of 120

    The point of intersection of the three altitudes of a triangle is called the:

    A Centroid B Incenter C Orthocenter D Circumcenter
99. Question 99 of 120

    The formula for the area of a sector subtending an angle θ at the center of a circle of radius r is:

    A (θ/360) × 2πr B (θ/180) × πr² C θ × πr² D (θ/360) × πr²
100. Question 100 of 120

     The sum of any two interior angles of a triangle is always:

     A Less than 180° B Equal to 180° C Greater than 180° D Equal to the third angle
101. Question 101 of 120

     The diameter of a circle is related to its radius by the formula:

     A d = 2r B d = r/2 C d = r² D d = πr
102. Question 102 of 120

     The sum of the interior angles of a triangle is always:

     A 90° B 270° C 180° D 360°
103. Question 103 of 120

     In a cyclic quadrilateral, one angle measures 70°. Find its opposite angle.

     A 70° B 90° C 110° D 180°
104. Question 104 of 120

     Two similar triangles have corresponding sides in the ratio 2:3. Find the ratio of their areas.

     A 2:3 B 4:9 C 4:6 D 8:27
105. Question 105 of 120

     An arc of a circle that is shorter than a semicircle (subtends an angle less than 180° at the center) is called a:

     A Major arc B Semicircular arc C Minor arc D Tangent arc
106. Question 106 of 120

     If two angles are each complementary to the same angle, then those two angles are:

     A Equal to each other B Supplementary to each other C Always 45° each D Vertically opposite
107. Question 107 of 120

     Find the area of a sector subtending a 60° angle at the center of a circle with radius 6 cm (leave your answer in terms of π).

     A 6π cm² B 3π cm² C 12π cm² D 36π cm²
108. Question 108 of 120

     The sum of all arcs that together make up a complete circle is:

     A 360° B 180° C 270° D It depends on the circle's radius
109. Question 109 of 120

     The Tangent-Chord Angle Theorem states that the angle between a tangent and a chord at the point of contact equals:

     A Half the central angle only B The angle in the alternate segment C 90° always D The angle subtended at the center
110. Question 110 of 120

     Each interior angle of a regular hexagon measures:

     A 100° B 110° C 135° D 120°
111. Question 111 of 120

     In any triangle, the longest side is always opposite the:

     A Smallest angle B Largest angle C Right angle only D It has no relation to the angles
112. Question 112 of 120

     Find the perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm.

     A 20 cm B 22 cm C 26 cm D 24 cm
113. Question 113 of 120

     Find the area of a circle with radius 14 cm (use π = 22/7).

     A 616 cm² B 308 cm² C 440 cm² D 704 cm²
114. Question 114 of 120

     Find the area of a triangle with base 10 cm and height 6 cm.

     A 16 cm² B 60 cm² C 40 cm² D 30 cm²
115. Question 115 of 120

     An angle that measures exactly 90° is called:

     A A right angle B A straight angle C A reflex angle D An acute angle
116. Question 116 of 120

     Two circles are said to be congruent if they have:

     A Equal areas only B The same center C Equal circumference but different radii D Equal radii
117. Question 117 of 120

     According to the Intersecting Chords Theorem, when two chords intersect inside a circle, the products of their respective segments are:

     A Never related B Equal only if the chords are equal in length C Always equal D Related only if both chords pass through the center
118. Question 118 of 120

     A line that intersects a circle at exactly two points is called a:

     A Tangent B Secant C Chord D Diameter
119. Question 119 of 120

     Two straight lines intersect. If one angle formed is 70°, find the angle vertically opposite to it.

     A 90° B 110° C 180° D 70°
120. Question 120 of 120

     Two angles whose sum is 180° are called:

     A Complementary angles B Corresponding angles C Alternate angles D Supplementary angles

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