Question

an equilateral triangle and an isosceles triangle share a common side. what is the measure of ∠abc? the measure of ∠abc is (square^{circ}). (simplify your answer.)

Explanation:

Step1: Identify triangle properties

In an equilateral triangle, all angles are 60°. In an isosceles - triangle, two angles are equal. Let's assume \(\triangle ABD\) is isosceles with \(\angle A = 61^{\circ}\) and \(\triangle BCD\) is equilateral.

Step2: Analyze the common - side situation

Since \(\triangle BCD\) is equilateral, \(\angle DBC=60^{\circ}\). In \(\triangle ABD\), if \(AB = BD\), then \(\angle ADB=\angle A = 61^{\circ}\), and \(\angle ABD=180^{\circ}-2\times61^{\circ}=58^{\circ}\).

Step3: Calculate \(\angle ABC\)

\(\angle ABC=\angle ABD+\angle DBC\). Substitute the values: \(\angle ABC = 58^{\circ}+60^{\circ}=118^{\circ}\).

Answer:

118