Complementary Angles Questions

Complementary Angles Questions is a helpful topic for students in learning how to find missing angles, basic equations and angle relationships in geometry. Complementary Angles Solution Regular practice builds confidence and accuracy for school exams and competitive tests. Complementary angles always add up to 90 °. These exercises help you apply the concept to various cases.

Complementary Angles Questions with Answers

Formula for Complementary Angles

Angle 1 + Angle 2 = 90°

If one angle = x, then its complement = 90° − x

Q1: One angle is 35°. Find its complement.

2D Diagram: Draw a right-angle corner (like the corner of a square). Inside the right angle, draw a line dividing it into two parts. Label one part 35° and the other "?°."

Solution: Missing angle = 90° − 35° = 55°

Q2: One angle is 72°. Find its complementary angle.

Solution: 90° − 72° = 18°

Q3: One angle is 45°. Find its complement.

Solution: 90° − 45° = 45°

Both angles are equal two 45° angles are complementary to each other.

Q4: Find the complement of 83°.

Solution: 90° − 83° = 7°

Q5: Which pairs are complementary? (a) 40° and 50° (b) 60° and 40° (c) 30° and 60°

Solution: (a) 40 + 50 = 90 Complementary (b) 60 + 40 = 100 Not complementary (c) 30 + 60 = 90 Complementary

Q6: ___° and 67° are complementary. Find the missing angle. Solution: 90 − 67 = 23°

Q7: 38° and ___° are complementary. Find the missing angle. Solution: 90 − 38 = 52°

Complementary Angles Algebra Questions

Solve for x

Q1: Two complementary angles are (3x + 5)° and (2x − 10)°. Find x and both angles.

Solution: (3x + 5) + (2x − 10) = 90 5x − 5 = 90 5x = 95 x = 19

Angle 1 = 3(19) + 5 = 62° Angle 2 = 2(19) − 10 = 28°

Check: 62 + 28 = 90°

Q2: Two complementary angles are (x + 15)° and (x − 5)°. Find x.

Solution: (x + 15) + (x − 5) = 90 2x + 10 = 90 2x = 80 x = 40

Angles: 55° and 35°

Q3: One complementary angle is three times the other. Find both.

Solution: Let smaller angle = x. Larger = 3x.

x + 3x = 90 4x = 90 x = 22.5°

Angles: 22.5° and 67.5°

Q4: The complement of an angle is 20° more than the angle itself. Find the angle.

Solution: Let angle = x. Complement = 90 − x.

90 − x = x + 20 70 = 2x x = 35°

Complement = 90 − 35 = 55°

Q5: Two complementary angles are in ratio 2 : 3. Find both.

Solution: 2k + 3k = 90 5k = 90 k = 18

Angles = 36° and 54°

Q6: Two complementary angles are in ratio 1 : 5. Find both angles.

Solution: k + 5k = 90 6k = 90 k = 15

Angles = 15° and 75°

Diagram Based Complementary Angles Questions

Q1: A right angle is divided into two parts by a ray. One part is 28°. Find the other.

Solution: 28 + ? = 90 ? = 62°

Q2: In a right-angled triangle, one acute angle is 52°. Find the other acute angle.

Solution: The two acute angles in a right-angled triangle are always complementary.

90 − 52 = 38°

Q3: Two angles together form a right angle. One angle is (4x)° and the other is (x + 5)°. Find both.

Solution: 4x + x + 5 = 90 5x = 85 x = 17

Angles: 4(17) = 68° and 17 + 5 = 22°

Check: 68 + 22 = 90°

Q4: Ray OC divides right angle AOB into two parts. Angle AOC = 3 × Angle COB. Find each angle.

Solution: Let angle COB = x. Then angle AOC = 3x.

3x + x = 90 4x = 90 x = 22.5°

Angle COB = 22.5°, Angle AOC = 67.5°

Complementary Angles Word Problems

Q1: A ladder leans against a wall making an angle of 62° with the ground. What angle does it make with the wall?

Solution: The angle with the wall + angle with the ground = 90° (right-angle triangle).

Angle with wall = 90 − 62 = 28°

Q2: A ramp rises at 18° from the ground. What angle does it make with a vertical wall at the top?

Solution: 18 + angle with wall = 90 Angle with wall = 72°

Q3: In a right-angled triangle ABC (right angle at C), angle A = (2x + 10)° and angle B = (x + 5)°. Find x and both angles.

Solution: A + B = 90 (complementary in a right triangle)

(2x + 10) + (x + 5) = 90 3x + 15 = 90 3x = 75 x = 25

Angle A = 60°, Angle B = 30°

Q4: Angle P and Angle Q are complementary. Angle Q and Angle R are also complementary. Prove Angle P = Angle R.

Solution: P + Q = 90 →P = 90 − Q Q + R = 90 → R = 90 − Q

Both P and R equal (90° − Q). Therefore P = R.

Complements of the same angle are always equal.

Multiple Choice Questions on Complementary Angles

Q1: Complement of 55° is: (a) 125° (b) 35° (c) 45° (d) 135°

Answer: (b) 35°

Q2: Two equal complementary angles. Each measures: (a) 90° (b) 60° (c) 45° (d) 30°

Answer: (c) 45°

Q3: Which pair is complementary? (a) 50°, 40° (b) 60°, 30° (c) 70°, 20° (d) 80°, 10°

Answer: (b) 60° + 30° = 90° (also (a), (c), (d) all are complementary ) All four options are complementary pairs.

Q4: Complement of an angle is four times itself. The angle is: (a) 18° (b) 20° (c) 22° (d) 24°

Answer: (a) 18° x + 4x = 90 → 5x = 90 → x = 18.

Q5: Two complementary angles are in ratio 4:5. The larger angle is: (a) 40° (b) 45° (c) 50° (d) 54°

Answer: (c) 50° 4k + 5k = 90 → k = 10. Larger = 5 × 10 = 50°.

Q6: If angle A = (x + 10)° and its complement = (2x − 4)°, find x: (a) 25 (b) 27 (c) 28 (d) 30

Answer: (c) 28 (x + 10) + (2x − 4) = 90 → 3x + 6 = 90 → x=28.

Q7: The complement of (90° − x) is: (a) x (b) 90°−x (c) 180°−x (d) x−90°

Answer: (a) x 90 − (90−x) = x.

Q8: If supplement of angle A = 130°, what is the complement of angle A? (a) 40° (b) 50° (c) 60° (d) 70°

Answer: (a) 40° A = 180−130 = 50°. Complement = 90 − 50 = 40°.

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