Question

1. 29° (11x - 65)°

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base angles are equal. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the triangle has two equal sides (marked), so the non - marked angle adjacent to \((11x - 65)^{\circ}\) is also \(29^{\circ}\). Then, by the exterior angle property: \(11x-65=29 + 29\)

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Answer:

\(x=\frac{123}{11}\approx11.18\)