Question

The angles which is four times more than its complement is
a) 120°
b) 144°
c) 150°
d) 100°
​

Answer 1

160

180-160 20

20x4 80

160 is greater than 80

Answer 2

The angle that is four times more than its complement is 72° .

• Let us consider 2 angles ∠A  and ∠B.

• We know that, for two angles to be complement, their sum should be equal to 90°.

• Thus, ∠A  + ∠B = 90°

∠B  = 90° -  ∠A

• Also, as per the question, the angle is 4 times its complement, thus,

∠A  = 4 ∠B

• Substituing the value of ∠B , we get,

∠A  = 4 ( 90° -  ∠A )

∠A = 360°  - 4∠A

5∠A  = 360°

∠A = 72°