Question

find the value of x in the triangle shown below.

x =

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (both are 6), it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\). We know one angle is \(58^{\circ}\). So, \(x + x+58^{\circ}=180^{\circ}\) (because the angles opposite the equal sides are equal). This simplifies to \(2x+58^{\circ}=180^{\circ}\).
Subtract \(58^{\circ}\) from both sides: \(2x=180^{\circ}- 58^{\circ}=122^{\circ}\).
Divide both sides by 2: \(x=\frac{122^{\circ}}{2}=61^{\circ}\).

Answer:

\(61\)