Practice Questions
Concept Explanation
Lines and angles form the basis of plane geometry. An angle measures rotation between two rays sharing a common vertex, in degrees (°).
Key Relationships
- Complementary angles sum to 90°.
- Supplementary angles sum to 180°.
- Vertically opposite angles are equal when two lines intersect.
- Linear pair on a straight line sums to 180°.
- Triangle angle sum = 180°.
Parallel Lines
When a transversal cuts parallel lines, corresponding angles are equal, alternate interior angles are equal, and co-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°).
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Q1 Easy
The complement of 35° is:
ExplanationComplement = 90° − 35° = 55°. -
Q2 Easy
The supplement of 120° is:
ExplanationSupplement = 180° − 120° = 60°. -
Q3 Easy
Two vertically opposite angles are each 70°. The other pair measures:
ExplanationVertically opposite angles are equal, so each is 70°. -
Q4 Easy
One angle of a linear pair is 65°. The other angle is:
ExplanationLinear pair sums to 180°: 180° − 65° = 115°. -
Q5 Easy
In a triangle, two angles are 50° and 60°. The third angle is:
ExplanationThird angle = 180° − 50° − 60° = 70°. -
Q6 Easy
A right angle measures:
ExplanationA right angle is exactly 90°. -
Q7 Easy
Angles on a straight line sum to:
ExplanationA straight angle equals 180°.
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Q8 Medium
If the complement of x is 25°, then x =
Explanationx + 25° = 90°, so x = 65°. -
Q9 Medium
If the supplement of x is 140°, then x =
Explanationx + 140° = 180°, so x = 40°. -
Q10 Medium
Two angles on a straight line are in ratio 2 : 3. The larger angle is:
Explanation2x + 3x = 180°, so x = 36°. Larger = 3 × 36° = 108°. -
Q11 Medium
Angles of a triangle are 2x, 3x and 4x. The largest angle is:
Explanation9x = 180°, so x = 20°. Largest = 4 × 20° = 80°. -
Q12 Medium
Corresponding angles are equal when two parallel lines are cut by a transversal. If one corresponding angle is 55°, its pair is:
ExplanationCorresponding angles are equal, so the pair is 55°. -
Q13 Hard
In an isosceles triangle, the vertex angle is 40°. Each base angle is:
ExplanationBase angles = (180° − 40°) / 2 = 70° each. -
Q14 Hard
An exterior angle of a triangle is 110°. If one remote interior angle is 50°, the other is:
ExplanationExterior angle = sum of remote interior angles: 110° − 50° = 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° − 100° = 80°. Statement II alone does not fix the two angles. -
DS2 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: 5x = 180°, so x = 36°. Statement II alone: 72° could be 2x or 3x.
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DS3 Easy
What is the complement of angle A?
Statement IA = 38°.
Statement IIThe supplement of A is 142°.
ExplanationEach alone gives A = 38°, so complement = 52°. -
DS4 Medium
What is each base angle of an isosceles triangle?
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 value.