Question

find the value of x.

Explanation:

Step1: Find the adjacent angle of \(149^{\circ}\)

The sum of adjacent angles on a straight line is \(180^{\circ}\). Let the adjacent angle be \(y\). Then \(y = 180^{\circ}- 149^{\circ}=31^{\circ}\)

Step2: Use the triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). We know two angles of the triangle: \(y = 31^{\circ}\) and \(113^{\circ}\), and the third angle is \(x\). So \(x+31^{\circ}+113^{\circ}=180^{\circ}\)

$$x=180^{\circ}-(31^{\circ}+113^{\circ})$$

$$x = 180^{\circ}-144^{\circ}$$

$$x = 36^{\circ}$$

Answer:

\(36\)