# Intersection of two rhombuses

In which way do two rhombuses have to intersect to form an octagon which has four angles equal to 150◦? All sides of the octagon are equal.

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Since you know that 4 of the angles have measure $150°$ and the sum of the measures of the interior angles of an octagon is $1080°$, consider that the other four angles might have measure $\frac{1}{4}(1080°-4\cdot150°)=120°$. That suggests using two congruent rhombuses with angles that measure $120°$ and $60°$—with congruent rhombuses, centered at the same point, and rotated 90° from one another, we will get all 8 sides of the octagon to have the same length. The octagon is the purple region of overlap in the diagram below.