Question

find the value of x.

Explanation:

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

The adjacent interior - angle and 137° form a linear pair. So, the adjacent interior - angle = 180° - 137° = 43°.

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

The sum of the interior angles of a triangle is 180°. Let the three interior angles of the triangle be \(x\), 105°, and 43°. Then \(x+105^{\circ}+43^{\circ}=180^{\circ}\).

Step3: Solve for \(x\).

\(x=180^{\circ}-(105^{\circ} + 43^{\circ})\)
\(x = 180^{\circ}-148^{\circ}\)
\(x = 32^{\circ}\)

Answer:

\(32^{\circ}\)