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.

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

$4x=60$

$x=\dfrac{60}{4}$

$x=15$

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.