Question

find the value of x. 50° a. 108° b. 50° c. 64° d. 80°

Explanation:

Step1: Identify isosceles triangle

The triangle has two equal - length sides (marked with red lines), so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the two equal angles be \(x\) and the third angle be 50°. So, \(x + x+50^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}- 50^{\circ}=130^{\circ}\).

Step3: Solve for \(x\)

Dividing both sides of \(2x = 130^{\circ}\) by 2, we get \(x=\frac{130^{\circ}}{2}=65^{\circ}\). But there is a mistake above. Since the angle of 50° is one of the base - angles, then \(x\) is the non - base angle. So \(x=180^{\circ}-2\times50^{\circ}\).

Step4: Calculate the value of \(x\)

\(x = 180^{\circ}-100^{\circ}=80^{\circ}\)

Answer:

d. \(80^{\circ}\)