Question

The measures of two supplementary angles are in the ratio 4 : 5. What are the measures of the angles?

Answer 1

Answer:

16:25

Step-by-step explanation:

Squaring both sides

Answer 2

Sum of two supplementary angles = 180°

The ratio of the measures of two supplementary angles =4:5

Total number of parts = 4+5 = 9

Which means :-

The measure of the first supplementary angle :-

$= \frac{4}{9} \: \: of \: \: 180$

$= \frac{4}{9} \times 180$

$= \frac{4 \times 180}{9}$

$= \frac{720}{9}$

$= \bold{80}°$

Thus, the measure of the first supplementary angle =80°

The measure of the second supplementary angle:-

$= \frac{5}{9} \: \: \: of \: \: \: 180$

$= \frac{5}{9} \times 180$

$= \frac{5 \times 180}{9}$

$= \frac{900}{9}$

$=\bold{ 100}°$

Thus, the measure of the second supplementary angle =100°

As the sum of both these angles is adding up to form 180°, we can conclude that we have found out the correct measure of each of the supplementary angles.

Therefore, the measure of the two supplementary angles are 80° and 100°