Question

the angles are complementry and the larger is four times the smaller

Answer 1

Let x and 90-x be the complementary angles

⇒ x=4(90-x)

⇒ x=72°

Required angles are 72° and 18°

Answer 2

let the complementary angles be x and y

sum of complementary angles = x + y = 90 deg....(1)

let the larger angle be 'x'

according to the question,

x = 4y.......(2)

substitute (2) in (1)

4y + y = 90

5y = 90

y (smaller angle) = 18 deg

x( larger angle) = 4(18) = 72 deg