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 5), 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 two equal angles be \(70^{\circ}\) (opposite the sides of length 5). Let the third angle be \(x\). Then \(70 + 70+x=180\).
Simplify the left - hand side: \(140 + x=180\).
Subtract 140 from both sides: \(x=180 - 140\).

Answer:

\(40\)