Question

1. △abc is isosceles, with \overline{ac} \cong \overline{ab}. solve for x.

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \( \triangle ABC\) with \( \overline{AC}\cong\overline{AB}\), the base - angles are equal. Let \( \angle C=\angle B = x\).

Step2: Apply the angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). So, \( \angle A+\angle B+\angle C = 180^{\circ}\). Given \( \angle A = 32^{\circ}\), and \( \angle B=\angle C=x\), we have the equation \(32 + x+x=180\).
Simplify the equation: \(32 + 2x=180\).
Subtract 32 from both sides: \(2x=180 - 32\).
\(2x = 148\).
Divide both sides by 2: \(x=\frac{148}{2}\).

Answer:

\(x = 74^{\circ}\)