Question

The complementary and supplementary angles of an angle are in ratio 2:5 respectively. Find the measure of that angle

Answer 1

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Answer 2

The Measure Of The Angle Is 30°

GIVEN

The ratio of the complementary and supplementary angles = 2:5

TO FIND

Measure of the angle.

SOLUTION

We can simply solve the above problem as Follows.

We know that,

The supplementary angles are angles whose sum = 180°

The complementary angle are angles whose sum = 90°

Let the angle be, x.

So,

x + supplementary angle = 180°

supplementary angle = 180-x

Similarly,

x + complementary angle = 90°

Complementary angle = 90-x

According to the question;

$\frac{90 - x}{180 - x} = \: \frac{2}{5}$

$450 - 5x = 360 - 2x$

$- 3x = - 90$

x = 30°

Hence, the measure of the angle is 30°

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