Question

For the following figure, find the value of $x$.

Short answer

The value of$x={53}^{\circ }$.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangles.

An isosceles triangle is a triangle that has two sides of equal length and two equal angles.

Step 3. Find the value.

Since the triangle is isosceles triangles thus$AB=AC=10$,$\angle BAC={74}^{\circ }$and $\angle BCA=x$.

$\angle ABC=\angle ACB=x$

Therefore, find the value of $x$as follows:

width="252">∠ABC+∠ACB+∠BAC=180∘x+x+74∘=180∘2x=180∘−74∘x=53∘

Therefore, the value of $x={53}^{\circ }$.