Question

find the value of x.

Explanation:

Step1: Find the interior - angle adjacent to 122°.

The adjacent interior - angle and 122° are supplementary. Let the adjacent interior - angle be $y$. Then $y + 122^{\circ}=180^{\circ}$, so $y = 180^{\circ}-122^{\circ}=58^{\circ}$.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is 180°. In the triangle, we know two angles: $y = 58^{\circ}$ and 81°. Let the third angle be $x$. Then $x+58^{\circ}+81^{\circ}=180^{\circ}$.

Step3: Solve for $x$.

$x=180^{\circ}-(58^{\circ}+81^{\circ})=180^{\circ}-139^{\circ}=41^{\circ}$.

Answer:

$41^{\circ}$