Problem 2. An isosceles trapezoid has bases $\overline{A B}=50 \mathrm{~cm}, \overline{C D}=20 \mathrm{~cm}$ and angle $\measuredangle B A D=60^{\circ}$. Find the perimeter of the trapezoid.
Solution. Let $D M \| B C$. Triangle AMD is equilateral because its angles are $\measuredangle A M D=60^{\circ}, \measuredangle A B C=60^{\circ}$ and $\measuredangle B A D=60^{\circ}$. Therefore, the segments $A D$ and $A M$ have a length of $30 \mathrm{~cm}$. For the perimeter, we get

$$
L=50+20+2 \cdot 30=130 \mathrm{~cm}
$$

![](https://cdn.mathpix.com/cropped/2024_06_05_bbda9f5c2f069cdaaac4g-08.jpg?height=339&width=462&top_left_y=1873&top_left_x=1026)