Question

1. given the isosceles triangle, find the value of x.

a. 16
b. 82
c. 98
d. 62

Explanation:

Step1: Find the base - angle of the isosceles triangle

The adjacent angle to \(98^{\circ}\) in the triangle is \(180^{\circ}-98^{\circ}=82^{\circ}\). Let's call this angle \(y = 82^{\circ}\).

Step2: Use the angle - sum property of a triangle

In an isosceles triangle, the two base - angles are equal. The sum of angles in a triangle is \(180^{\circ}\). Let the vertex angle be \(x\).
We know that \(x + 2y=180^{\circ}\) (since the triangle is isosceles, the two base - angles are equal). Substitute \(y = 82^{\circ}\) into the equation:
\(x+2\times82^{\circ}=180^{\circ}\)
\(x + 164^{\circ}=180^{\circ}\)
\(x=180^{\circ}-164^{\circ}\)
\(x = 16^{\circ}\)

Answer:

A. 16