Question

triangle abc, shown in the diagram below, is an isosceles triangle. if the measure of ∠cab is 15°, what is the measure of ∠abc? 82.5° 75° 165° 15°

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle $\triangle ABC$ 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 $\angle CAB = 15^{\circ}$. Then $x + x+15^{\circ}=180^{\circ}$.

Step3: Solve the equation

Combining like - terms, we get $2x=180^{\circ}- 15^{\circ}=165^{\circ}$. Then $x=\frac{165^{\circ}}{2}=82.5^{\circ}$.

Answer:

$82.5^{\circ}$