**Word Problems**

**Q1.** Two angles are complementary. If one of the angles is double the other angle, find the two angles.

**Ans:** 30° and 60°

**Q2.** Two angles are complementary. If one angle is two times the sum of other angle and 3, find the two angles.

**Ans:** 62° and 28°

**Q3.** The measure of an angle is ¾ of 60°. What is the measure of the complementary angle?

**Ans:** 45°

**Q4.** Two angles are supplementary. If one angle is 36° less than twice of the other angle, find the two angles.

**Ans:** 108° and 72°

**Q5.** An angle and its one-half are complementary. Find the angle.

**Ans:** 60°.

**Q6.** Two angles are supplementary. If 5 times of one angle is 10 times of the other angle. Find the two angles.

**Ans:** 60° and 120°.

**Q7.** The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle of A. What is the sum in degrees, of the measures of the supplement and complement of angle A?

**Ans:** 190°

**Q8.** Twice the complement of an angle is 24 degrees less than its supplement. What is the measure of the angle?

**Ans:** 24 degrees°

**Q9.** Two angles are supplementary. If the ratio of the measure of the smaller angle to that of the larger angle is 5:7, what is the measure of the smaller angle?

**Ans:** 75°.

**Q10.** The measure of supplement of an angle is equal to the twice the measure of the angle. What is the measure in degrees, of the compliment of the angle?

**Ans:** 30°

**Q11.** If 4 times the sum of an angle and 5 is 32, find the type of the angle.

**Ans:** Obtuse angle

**Q12.** If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

**Ans:** Reflex angle

**Q13.** If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

**Ans:** Right angle

**Q14.** If 7 times the difference between 3 times of an angle and 5 is 3745, find the type of the angle.

**Ans:** Straight angle

**Q15.** If 2 times the difference between 9 times of angle and 15 is 6450, find the type of the angle.

**Ans:** Full angle

**Q16. **In a triangle, the ratio between the first and second angle is 1:2 and the third angle is 72. Find the first and second angle of the triangle.

**Ans: **36° and 72°

**Q17. **In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 3, find the three angles of the triangle.

**Ans:** 28°, 93° and 59°

**Q18.** In a right triangle, apart from the right angle, the other two angles are x + 1 and 2x + 5. Find the angles of the triangle.

**Ans:** Hence 90°, 29° and 61°

**Q19.** In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

**Ans:** 30°, 60° and 90°

**Q20.** If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

**Ans:** 59°, 60° and 61°

**Box**

**Did you know? **

Complementary angles are two angles with a sum of 90∘. A common case is when they form a right angle. Supplementary angles, on the other hand, are two angles with a sum of 180∘. A common case is when they lie on the same side of a straight line.