Question

triangle abc, shown in the diagram below, is an isosceles triangle where $overline{ab}congoverline{ac}$. what is the measure, in degrees, of $angle abc? 84^{circ} 43^{circ} 123^{circ} 57^{circ}$

Explanation:

Step1: Find adjacent - interior angle

The adjacent - interior angle to the 123 - degree exterior angle at point C is $180 - 123=57^{\circ}$.

Step2: Use isosceles - triangle property

Since $\overline{AB}\cong\overline{AC}$, $\angle ABC=\angle ACB$. And we found $\angle ACB = 57^{\circ}$, so $\angle ABC = 57^{\circ}$.

Answer:

$57^{\circ}$