Question

1. in triangle abc, the measure of angle b is 50°. find the measure of angle a.

Explanation:

Step1: Identify the triangle type

Since two sides of triangle \(ABC\) are marked as equal, it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So, \(\angle B=\angle C = 50^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\angle A=x\). Then, by the angle - sum property of a triangle \(x+\angle B+\angle C=180^{\circ}\).
Substitute \(\angle B = 50^{\circ}\) and \(\angle C = 50^{\circ}\) into the equation: \(x + 50^{\circ}+50^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(x+100^{\circ}=180^{\circ}\).
Subtract \(100^{\circ}\) from both sides: \(x=180^{\circ}- 100^{\circ}\).

Answer:

\(80^{\circ}\)