Question

Two angles are supplementary. One measures 3x-2 and the other measures 2x+7 Find the value of x and the measure of the smaller angle.

Answer 1

Sum of two angles that are supplementary = 180°

Then :-

`3x - 2 + 2x+ 7 = 180`

`5x + 5 = 180`

`5x = 180 - 5`

`5x = 180 - 5`

`5x = 175`

`x = (175)/(5)`

`x = 35`

Which means :-

The measure of the larger angle :-

= 35 × 3 - 2

= 105 - 2

= 103°

The measure of the smaller angle :-

= 2 × 35 + 7

= 70 + 7

= 77°

Therefore , the value of x = 35 and the measure of the smaller angle = 77° .