Question

29° (11x - 65)°

Explanation:

Step1: Use the exterior angle property of an isosceles triangle

In an isosceles triangle, the exterior angle is equal to the sum of the two non - adjacent interior angles. Here, the two non - adjacent interior angles are \(29^{\circ}\) and \(29^{\circ}\) (since the triangle has two equal sides, the base angles are equal). So, \(11x - 65=29 + 29\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side of the equation: \(29+29 = 58\). Then we have the equation \(11x-65 = 58\). Add \(65\) to both sides of the equation: \(11x=58 + 65\). So, \(11x=123\). Divide both sides by \(11\): \(x=\frac{123}{11}\approx11.18\). But wait, there's a mistake. Let's re - check.

Wait, actually, in an isosceles triangle, the exterior angle \((11x - 65)^{\circ}\) is equal to the sum of the two equal base angles. The correct equation is \(11x-65=29+(29)\).

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Answer:

\(x = 13\)