Question

Two complementary angles differ by 20°. Find the angles.

Answer 1

Let one of the angles be x, then the other will be x – 20°.

According to the question,

x + (x – 20°) = 90°  .......[∵ Sum of complementary angles is 90°]

⇒ x + x – 20° = 90°

⇒ 2x – 20° = 90°

⇒ 2x = 90° + 20°  .......[Transposing (– 20°) to RHS]

⇒ 2x = 110°

⇒ `(2x)/2 = 110^circ/2`  .......[Dividing both sides by 2]

⇒ x = 55°

Hence, the required angles are 55° and (55 – 20)° i.e. 55° and 35°.