Question

1. consider the diagram below. 5a first, solve for x. enter your next step here

Explanation:

Step1: Find \( y \)

Use the exterior angle theorem for the smaller triangle. The exterior angle \( 66^{\circ}=31^{\circ}+y^{\circ} \), so \( y = 66 - 31=35 \).

Step2: Solve for \( x \)

Use the triangle angle - sum theorem for the larger triangle. The sum of angles in a triangle is \( 180^{\circ} \). So \( x+31+(y + 79)=180 \). Substitute \( y = 35 \) into the equation: \( x+31+(35 + 79)=180 \). Simplify the left - hand side: \( x+31 + 114=180 \), then \( x+145 = 180 \). Subtract 145 from both sides: \( x=180 - 145 \).

Answer:

\( x = 35 \)