Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
up vote 3 down vote accepted

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.

overlapping rhombi graphics

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.