Question

find the value of x in the triangle shown below.

x =

Explanation:

Step1: Identify the triangle type

This is an isosceles triangle (two sides of length \(4\)). In an isosceles triangle, the angles opposite the equal sides are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the two equal angles be \(x\) and the third angle be \(56^{\circ}\). Then \(x + x+56^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}- 56^{\circ}\).
So, \(2x = 124^{\circ}\), and \(x=\frac{124^{\circ}}{2}\).

Answer:

\(62\)