Question

a side of the triangle below has been extended to form an exterior angle of 157°. find the value of x. answer attempt 1 out of 2 x =

Explanation:

Step1: Find the adjacent interior angle

The sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). Let the adjacent interior angle be \(y\). Then \(y + 157^{\circ}=180^{\circ}\), so \(y=180^{\circ}- 157^{\circ}=23^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). In the triangle, we know two angles: one is \(y = 23^{\circ}\) and another is \(102^{\circ}\), and the third angle is \(x\). So \(x+23^{\circ}+102^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(23^{\circ}+102^{\circ})$$

$$x = 180^{\circ}-125^{\circ}$$

Answer:

\(x = 55\)