Question

what is the value of x? show your work.
solution

Explanation:

Step1: Find interior adjacent angles

First, calculate the interior angles supplementary to the given exterior angles:
For the 163° angle: $180^\circ - 163^\circ = 17^\circ$
For the 89° angle: $180^\circ - 89^\circ = 91^\circ$

Step2: Sum interior angles of triangle

The sum of interior angles in a triangle is $180^\circ$. Set up the equation:
$17^\circ + 91^\circ + 2x^\circ = 180^\circ$

Step3: Simplify and solve for x

Combine known angles:
$108^\circ + 2x^\circ = 180^\circ$
Subtract $108^\circ$ from both sides:
$2x = 180 - 108 = 72$
Divide by 2:
$x = \frac{72}{2} = 36$

Answer:

$x = 36$