Question

find the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be $y$. Then $y+39^{\circ}+82^{\circ}=180^{\circ}$.

Step2: Solve for $y$

$y = 180^{\circ}-(39^{\circ}+82^{\circ})=180^{\circ}-121^{\circ}=59^{\circ}$.

Step3: Use the linear - pair property

The angle $x$ and $y$ form a linear pair. Since the sum of angles in a linear pair is 180°, and $y = 59^{\circ}$, then $x=180^{\circ}-y$.

Step4: Calculate $x$

$x = 180^{\circ}-59^{\circ}=121^{\circ}$.

Answer:

$121$