Question

find the value of x.

Explanation:

Step1: Find the interior - angle adjacent to 137°.

The sum of an interior - angle and its adjacent exterior - angle of a triangle is 180°. Let the interior - angle adjacent to 137° be $y$. Then $y + 137^{\circ}=180^{\circ}$, so $y = 180^{\circ}-137^{\circ}=43^{\circ}$.

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 one angle is 86° and another is $y = 43^{\circ}$, and the third angle is $x$. So $x+86^{\circ}+43^{\circ}=180^{\circ}$.

Step3: Solve for $x$.

$x=180^{\circ}-(86^{\circ}+43^{\circ})=180^{\circ}-129^{\circ}=51^{\circ}$.

Answer:

$x = 51$