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

Question

Accepted Answer

# Explanation:
## Step1: Analyze triangle $ABD$
Since $ABD$ is an isosceles triangle ($AB = BD$), $\angle A=\angle BDA = 67^{\circ}$. Using the angle - sum property of a triangle ($\angle A+\angle BDA+\angle ABD=180^{\circ}$), we can find $\angle ABD$.
$$
\begin{align*}
\angle ABD&=180^{\circ}-(67^{\circ}+ 67^{\circ})\
&=180^{\circ}-134^{\circ}\
&=46^{\circ}
\end{align*}
$$
## Step2: Analyze triangle $BCD$
Since $BCD$ is an equilateral triangle, $\angle CBD = 60^{\circ}$ (all angles in an equilateral triangle are $60^{\circ}$).
## Step3: Calculate $\angle ABC$
Using the angle - addition property ($\angle ABC=\angle ABD+\angle CBD$)
$$
\begin{align*}
\angle ABC&=46^{\circ}+60^{\circ}\
&=106^{\circ}
\end{align*}
$$

# Answer:
$106$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Analyze triangle \(ABD\)

Step2: Analyze triangle \(BCD\)

Step3: Calculate \(\angle ABC\)

Answer: