Question

a side of the triangle below has been extended to form an exterior angle of $129^{circ}$. find the value of $x$.
(there is a triangle in the image, with one angle marked $x^{circ}$, another angle marked $112^{circ}$, and an exterior angle marked $129^{circ}$)

Explanation:

Step1: Find the adjacent interior angle

The exterior angle and its adjacent interior angle are supplementary, so the adjacent interior angle is $180^\circ - 129^\circ = 51^\circ$.

Step2: Use the triangle angle sum property

The sum of the interior angles of a triangle is $180^\circ$. Let the three angles be $x^\circ$, $112^\circ$, and $51^\circ$. So $x + 112 + 51 = 180$.

Step3: Solve for x

Simplify the equation: $x + 163 = 180$. Subtract 163 from both sides: $x = 180 - 163 = 17$.

Answer:

$x = 17$