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