Question

The ratio of measure of complementary angle of one angle with its measure of supplementary angle is 2:5, then what will be the ratio of that angle with its supplementary angle?

a) 1:10
b)1:5
c)3:10
d)1:15

Plz give answer fast....

Answer 1

Given :Measure of supplementary angle = 2:5

To find : Ratio of angle with the supplementary angle

Solution:

Let the angle be = x

The supplementary angle = 180–x

The complementary angle = 90-x

According to the question -

(180-x) /(90- x) = 2/5

2 (180-x) = 5 (90- x)

360 – 2 x = 450 – 5x

360 - 450 = -5x + 2x

- 90 = -3x

x = 30

Thus,  the supplementary = 180 - 30 = 150

= Angle : Supplementary angle = 30 : 150

= 1:5 ( Answer)

Answer 2

Given :

The ratio of measure of complementary angle of one angle with its measure of supplementary angle is = 2 : 5

To Find:

The ratio of that angle with its supplementary angle

Solution:

Let The angle = x

∵ For complementary angle , The sum of two angles = 90°

So, one angle = 90° - x

And For supplementary angle , The sum of two angles = 180°

So, one angle = 180° - x

According to question

$\dfrac{90^{\circ}-x}{{180^{\circ}-x}}$  = $\dfrac{2}{5}$

By cross multiplication

  5 ( 90° - x ) = 2 ( 180° - x )

Or,  450° - 5 x = 360° - 2 x

Or, 5 x - 2 x = 450° -  360°

Or,         3 x = 90°

∴              x = $\dfrac{90^{\circ}}{3}$

i.e             x = 30°

So, The value of angle = x = 30°

And, The measure of supplementary angle = 180°- 30°  = 150°

So, The ratio of angle with supplementary angle = 30° : 150°

Hence, The ratio of angle with its supplementary angle is 1 : 5     Answer