Question

1. find ( mangle a ) (click here for video #5)

Explanation:

Step1: Use the property of isosceles triangle

Since \(AC = AB\), \(\angle C=\angle B = 2x^{\circ}\)

Step2: Apply the triangle - angle sum theorem

The sum of interior angles of a triangle is \(180^{\circ}\). So \(4x + 2x+2x=180\)
Simplify the left - hand side: \(8x = 180\)
Solve for \(x\): \(x=\frac{180}{8}=22.5\)

Step3: Calculate \(m\angle A\)

Substitute \(x = 22.5\) into \(4x\). Then \(m\angle A=4x=4\times22.5 = 90^{\circ}\)

Answer:

\(90^{\circ}\)