Practice Questions
Concept Explanation
Lines and angles are the foundation of plane geometry. An angle is the amount of turn between two rays from a common vertex, measured in degrees (°).
Key Relationships
- Complementary angles add to 90°.
- Supplementary angles add to 180°.
- Vertically opposite angles are equal when two lines intersect.
- Linear pair on a straight line sums to 180°.
- Angle sum in a triangle is always 180°.
Parallel Lines and Transversals
When a transversal cuts two parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-interior (same-side interior) angles are supplementary.
Example
If one angle of a linear pair is 65°, the other is 180° − 65° = 115°.
Common Trap
Do not confuse complementary (90°) with supplementary (180°). Also remember that an exterior angle of a triangle equals the sum of the two remote interior angles.
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Q1 EasyThe complement of 35° is:ExplanationComplement means the angle that adds with 35° to make 90°. Required angle = 90° − 35° = 55°. Hence the answer is 55°.
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Q2 EasyOne angle of a linear pair is 65°. The other angle is:ExplanationAngles on a straight line sum to 180°. Other angle = 180° − 65° = 115°. Hence the answer is 115°.
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Q3 EasyTwo vertically opposite angles are each 70°. The other pair measures:ExplanationWhen two lines intersect, vertically opposite angles are equal in measure. If one pair is 70° each, the opposite pair is also 70° each. Hence the answer is 70° each.
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Q4 EasyThe supplement of 120° is:ExplanationSupplement = 180° − given angle = 180° − 120° = 60°. Hence the answer is 60°.
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Q5 EasyIn a triangle, two angles are 50° and 60°. The third angle is:ExplanationSum of angles in a triangle = 180°. Third angle = 180° − 50° − 60° = 70°. Hence the answer is 70°.
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Q6 EasyA right angle measures:ExplanationA right angle is defined as exactly 90°. Hence the answer is 90°.
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Q7 EasyAngles on a straight line sum to:ExplanationA straight line forms a straight angle of 180°, so adjacent angles on it sum to 180°. Hence the answer is 180°.
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Q8 MediumIf the complement of x is 25°, then x =ExplanationComplement of x is 90° − x. So 90° − x = 25°, giving x = 65°. Hence the answer is 65°.
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Q9 MediumIf the supplement of x is 140°, then x =Explanationx + 140° = 180°, so x = 40°. Hence the answer is 40°.
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Q10 MediumTwo angles on a straight line are in ratio 2 : 3. The larger angle is:ExplanationLet angles be 2x and 3x. Then 5x = 180°, x = 36°, larger = 3 × 36° = 108°. Hence the answer is 108°.
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Q11 MediumAngles of a triangle are 2x, 3x and 4x. The largest angle is:Explanation2x + 3x + 4x = 180° ⇒ 9x = 180° ⇒ x = 20°. Largest = 4x = 80°. Hence the answer is 80°.
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Q12 MediumCorresponding angles are equal when parallel lines are cut by a transversal. If one corresponding angle is 55°, its pair is:ExplanationCorresponding angles are equal when lines are parallel, so the pair is 55°. Hence the answer is 55°.
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Q13 HardIn an isosceles triangle, the vertex angle is 40°. Each base angle is:ExplanationBase angles are equal. Each = (180° − 40°) / 2 = 70°. Hence the answer is 70°.
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Q14 HardAn exterior angle of a triangle is 110°. If one remote interior angle is 50°, the other is:ExplanationExterior angle equals sum of remote interior angles. So other interior = 110° − 50° = 60°. Hence the answer is 60°.
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DS1 Easy
What is the third angle of a triangle?
Statement ITwo angles are 45° and 55°.
Statement IIThe sum of two angles is 100°.
ExplanationStatement I alone: third angle = 180° − 45° − 55° = 80°. Statement II alone gives only the sum of two angles, not their individual measures, so the third angle is not fixed. Answer: A. -
DS2 Easy
What is the complement of angle A?
Statement IA = 38°.
Statement IIThe supplement of A is 142°.
ExplanationStatement I alone: complement = 90° − 38° = 52°. Statement II alone: A = 180° − 142° = 38°, so complement = 52°. Each alone is sufficient. Answer: D.
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DS3 Medium
What is x if 2x and 3x form a linear pair?
Statement IThe angles are in ratio 2 : 3.
Statement IIOne of the angles is 72°.
ExplanationStatement I alone: 2x + 3x = 180°, so 5x = 180° and x = 36°. Statement II alone: 72° could be 2x or 3x, giving different x. Answer: A. -
DS4 Medium
For each base angle of an isosceles triangle. What is each base angle?
Statement IThe vertex angle is 50°.
Statement IIThe base angles are equal.
ExplanationStatement I alone: each base angle = (180° − 50°) / 2 = 65°. Statement II alone does not give a numeric vertex angle. Answer: A.