Question

find the value of x.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. First, find the third - interior angle of the triangle. Let the third - interior angle be $y$. So, $y+46^{\circ}+79^{\circ}=180^{\circ}$.

Step2: Solve for $y$

$y = 180^{\circ}-(46^{\circ}+79^{\circ})=180^{\circ}-125^{\circ}=55^{\circ}$.

Step3: Use linear - pair property

The angle $x$ and the interior angle $y$ form a linear pair. A linear pair of angles sums to 180°. So, $x + y=180^{\circ}$.

Step4: Solve for $x$

Since $y = 55^{\circ}$, then $x=180^{\circ}-55^{\circ}=125^{\circ}$.

Answer:

$125$