Question

triangle abc, shown in the diagram below, is an isosceles triangle. if the measure of ∠cab is 25°, what is the measure of ∠abc? 25° 77.5° 155° 65°

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle \(ABC\) with \(AC = AB\), \(\angle ABC=\angle ACB\).

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let \(\angle ABC = x\) and \(\angle ACB=x\), and \(\angle CAB = 25^{\circ}\). Then \(x + x+25^{\circ}=180^{\circ}\), which simplifies to \(2x=180^{\circ}- 25^{\circ}=155^{\circ}\).

Step3: Solve for \(x\)

Dividing both sides of \(2x = 155^{\circ}\) by 2, we get \(x=\frac{155^{\circ}}{2}=77.5^{\circ}\).

Answer:

\(77.5^{\circ}\)