1
Two angles of a triangle are 48° and 67°. What is the third angle?
Correct answer: D. 65°
The angles of a triangle add up to 180°: 180 − 48 − 67 = 65°.
easy
Geometry and Trigonometry MCQs
Solved MCQs on triangles, polygons, Pythagoras, angles, cones and standard trigonometric values and identities, as asked in SSC CGL and CHSL.
20 MCQsUpdated 27 October 2026
This set covers the angles of triangles and polygons, areas of standard figures, complementary and supplementary angles, and the trigonometric ratios of standard angles such as 30°, 45° and 60°.
Learn the table of trigonometric values for 0°, 30°, 45°, 60° and 90° until you can write it from memory. It answers a large share of trigonometry questions directly.
- 2
What is the sum of the interior angles of a heptagon (7 sides)?
Correct answer: C. 900°
Sum = (n − 2) × 180° = 5 × 180° = 900°.
medium - 3
What is each interior angle of a regular octagon?
Correct answer: D. 135°
Each exterior angle = 360° ÷ 8 = 45°, so each interior angle = 180° − 45° = 135°.
medium - 4
What is each interior angle of a regular hexagon?
Correct answer: D. 120°
Each exterior angle = 360° ÷ 6 = 60°, so each interior angle = 120°.
easy - 5
Each exterior angle of a regular polygon is 24°. How many sides does it have?
Correct answer: C. 15
The exterior angles add up to 360°, so the number of sides = 360 ÷ 24 = 15.
medium - 6
The two shorter sides of a right-angled triangle are 9 cm and 40 cm. What is the hypotenuse?
Correct answer: A. 41 cm
Hypotenuse = √(9² + 40²) = √(81 + 1600) = √1681 = 41 cm.
medium - 7
In a right-angled triangle the hypotenuse is 25 cm and one side is 7 cm. Find the other side.
Correct answer: A. 24 cm
Other side = √(25² − 7²) = √(625 − 49) = √576 = 24 cm.
medium - 8
What is the length of the diagonal of a square of side 8 cm?
Correct answer: D. 8√2 cm
Diagonal = side × √2 = 8√2 cm (about 11.31 cm).
easy - 9
What is the area of an equilateral triangle with side 10 cm?
Correct answer: D. 25√3 cm²
Area = (√3/4) × side² = (√3/4) × 100 = 25√3 cm².
medium - 10
What is the value of sin 30°?
Correct answer: A. 1/2
sin 30° = 1/2. (sin 60° = √3/2 and sin 45° = 1/√2.)
easy - 11
What is the value of tan 45°?
Correct answer: B. 1
tan 45° = sin 45° ÷ cos 45° = 1.
easy - 12
What is the value of cos 60°?
Correct answer: B. 1/2
cos 60° = 1/2, the same as sin 30°.
easy - 13
What is the value of tan 60°?
Correct answer: A. √3
tan 60° = sin 60° ÷ cos 60° = (√3/2) ÷ (1/2) = √3.
easy - 14
What is the value of sin²37° + cos²37°?
Correct answer: C. 1
For every angle θ, sin²θ + cos²θ = 1.
easy - 15
What is the value of sec²θ − tan²θ?
Correct answer: D. 1
From 1 + tan²θ = sec²θ, it follows that sec²θ − tan²θ = 1.
medium - 16
What is the value of sin 30° + cos 60°?
Correct answer: A. 1
sin 30° = 1/2 and cos 60° = 1/2, so the sum is 1.
easy - 17
What is the complement of an angle of 35°?
Correct answer: B. 55°
Complementary angles add up to 90°: 90 − 35 = 55°.
easy - 18
What is the supplement of an angle of 112°?
Correct answer: C. 68°
Supplementary angles add up to 180°: 180 − 112 = 68°.
easy - 19
The angle in a semicircle is always:
Correct answer: D. 90°
An angle drawn from the ends of a diameter to any point on the circle is always 90° (Thales' theorem).
medium - 20
A cone has radius 7 cm and height 24 cm. What is its slant height?
Correct answer: C. 25 cm
Slant height = √(r² + h²) = √(49 + 576) = √625 = 25 cm.
medium