The figure is formed by 5 equal isosceles trapezoids. What is the measure of the indicated angle?

![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-10.jpg?height=140&width=286&top_left_y=1192&top_left_x=791)
A) $72^{\circ}$
B) $74^{\circ}$
C) $76^{\circ}$
D) $78^{\circ}$
E) $80^{\circ}$

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Solution

## ALTERNATIVE A

We recall that the sum of the interior angles of a polygon with $n$ sides is $(n-2) \times 180^{\circ}$. We can view the figure in the statement as a polygon with 6 sides (in a thicker line in the figure below); the sum of its interior angles is then $(6-2) \times 180^{\circ}=720^{\circ}$. On the other hand, since the trapezoids are congruent, the sum of these interior angles is equal to 10 times the measure of the marked angle, which is then $\frac{720^{\circ}}{10}=72^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_01_984603b876c0bc28095bg-32.jpg?height=194&width=368&top_left_y=708&top_left_x=747)