Question

find the magnitude of an angle which is 2/3 of its supplement

Answer 1

Let the first angle be `x`
Then the other angle will be 2/3 of x = 2x/3
According to the Q
⇒x + 2x/3 = 180    [supplementary]
⇒(3x+2x)/3 = 180
⇒5x = 180 ×3
⇒x = 540/5
∴x= 108°
∴The required angle = 2x/3
                                 = 2(108)/3 
                                 = 216/3
                                 = 72°

Answer 2

Given : An angle which is 2/3 of its supplement.

To find : The said angle.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the magnitude of the said angle)

We know that,

If the sum of two angles becomes equal to 180° then they are called supplementary angles.

Let, the supplement of the said angle = x°

The said angle :

= x° × (2/3)

= 2x°/3

According to the previously mentioned mathematical formula, we get :

x + (2x/3) = 180

(3x + 2x)/3 = 180

5x = 180 × 3

x = (180 × 3)/5

x = 108

So,

The supplement of the said angle = x° = 108°

And,

The said angle = (2 × x°)/3 = (2 × 108°)/3 = 72°

(This will be considered as the final result.)

Hence, the said angle is 72°