Question

Two angles are in the ratio 4:9 and their supplementary angles are in the ratio 8:3 then the two angles are respectively. A) 60,135 B) 30,80 C) 40,90 D) 80,30

Answer 1

Answer:

Step-by-step explanation:

60°, 135°

Answer 2

Answer:

The two angles are 60° and 135°

Step-by-step explanation:

let the x and y be the required angles

The ratio of two angles is 4:9

Therefore,

$\frac{x}{y} =\frac{4}{9}$

$y = \frac{9x}{4}$ → (1)

The supplementary angle of x is (180 - x), and that of y is (180 - y)

The ratio of supplementary angles is 8:3

Therefore,

$\frac{180-x}{180-y}=\frac{8}{3}$ → (2)

put the value of y in equation (2)

$\frac{180-x}{180-\frac{9x}{4} }=\frac{8}{3}$

$(180-x)3=8(180-\frac{9x}{4} )$

540 - 3x = 1440 - 18x

15x = 900

x = 60

put x = 60 in equation (1)

$y = \frac{9(60)}{4}$

y = 135

Therefore the required angles are 60° and 135°