Question

An angle is 5 times of its supplementary angle, the measure of the smaller angle is _____​

Answer 1

Answer:

The measure of the smaller angle is 30°.

Step-by-step explanation:

Given :

An angle is 5 times of its supplementary angle.

To find :

the measure of the smaller angle

Solution :

When the sum of two angles is equal to 180°, they are said to be supplementary angles.

Let the angle be x°

It's supplementary angle = (180 - x)°

According to the question,

x° = 5(180 - x)°

x° = 900 - 5x°

x° + 5x° = 900°

6x = 900°  

 x = 900/6

 x = 150°

The angle is 150°.

>> It's supplementary angle = 180 - 150 = 30°

Therefore, the measure of the smaller angle is 30°.

Answer 2

Solution ↓

→ We know that supplementary angle are those angles which are formed when sum of 2 angles is 180°.

→ Let the smaller angle be a, then

other angle = 5 × a.

» » According to question :-

→ Angle A + Angle B = 180°

→ a + (5 × a) = 180°

→ a + 5a = 180°

→ 6a = 180°

→ a = (180 ÷ 6)°

→ a = 30° (Ans)

Therefore, we have found that measure of smaller angle is 30°.