Given:
In a right angle triangle, the measure of exterior angle is [tex](9x+16)^\circ[/tex].
The measure of opposite interior angle is [tex](5x-14)^\circ[/tex].
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
[tex](9x+16)^\circ=90^\circ+(5x-14)^\circ[/tex]
[tex](9x+16)^\circ=(5x+76)^\circ[/tex]
[tex]9x+16=5x+76[/tex]
Isolate the variable x.
[tex]9x-5x=-16+76[/tex]
[tex]4x=60[/tex]
[tex]x=\dfrac{60}{4}[/tex]
[tex]x=15[/tex]
The value of x is 15. So, the measure of the exterior angle is:
[tex](9x+16)^\circ=(9(15)+16)^\circ[/tex]
[tex](9x+16)^\circ=(135+16)^\circ[/tex]
[tex](9x+16)^\circ=151^\circ[/tex]
Therefore, the value of x is 15 and the measure of the exterior angle is 151 degrees.
