Question

10.
29°
(11x - 65)°

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base angles are equal. The sum of interior angles of a triangle is \(180^{\circ}\). So, \(29+(4x + 8)+(11x-65)=180\).

Step2: Simplify the equation

First, combine like - terms: \(29 + 4x+8+11x - 65=180\), which simplifies to \((4x + 11x)+(29 + 8-65)=180\), then \(15x+(37 - 65)=180\), and further \(15x-28 = 180\).

Step3: Solve for \(x\)

Add \(28\) to both sides of the equation: \(15x-28+28=180 + 28\), getting \(15x=208\). Then divide both sides by \(15\): \(x=\frac{208}{15}\approx13.87\).

Answer:

\(x=\frac{208}{15}\)