Question

I need to find the value of x and the measure of the exterior angle

Answer 1

Given:

In a right angle triangle, the measure of exterior angle is
`(9x+16)^\circ`.

The measure of opposite interior angle is
`(5x-14)^\circ`.

To find:

The value of x.

Solution:

Exterior angle theorem: In a triangle the measure of an exterior angle is equal to the measure of sum of two interior angles.

Using exterior angle theorem, we get

`(9x+16)^\circ=90^\circ+(5x-14)^\circ`

`(9x+16)^\circ=(5x+76)^\circ`

`9x+16=5x+76`

Isolate the variable x.

`9x-5x=-16+76`

`4x=60`

`x=(60)/(4)`

`x=15`

The value of x is 15. So, the measure of the exterior angle is:

`(9x+16)^\circ=(9(15)+16)^\circ`

`(9x+16)^\circ=(135+16)^\circ`

`(9x+16)^\circ=151^\circ`

Therefore, the value of x is 15 and the measure of the exterior angle is 151 degrees.