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 - side markings, so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use angle - sum property of 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 \(2x=180^{\circ}- 50^{\circ}\).

Step3: Solve for \(x\)

\(2x = 130^{\circ}\), then \(x=\frac{130^{\circ}}{2}=65^{\circ}\). But there is a mistake above. Since the angle of 50° is one of the base - angles, the other base - angle is also 50°. Then \(x = 180^{\circ}-2\times50^{\circ}\).

Step4: Calculate final value of \(x\)

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

Answer:

d. 80°