Question

find the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be $y$. So, $y+52^{\circ}+80^{\circ}=180^{\circ}$.

Step2: Calculate the third - interior angle $y$

$y = 180^{\circ}-(52^{\circ}+80^{\circ})=180^{\circ}-132^{\circ}=48^{\circ}$.

Step3: Use the linear - pair property

The angle $x$ and the third - interior angle $y$ form a linear pair. Since the sum of angles in a linear pair is 180°, we have $x + y=180^{\circ}$. Substituting $y = 48^{\circ}$, we get $x=180^{\circ}-48^{\circ}$.

Answer:

$132^{\circ}$