2021 JMPSC Sprint Problems/Problem 3

Problem

If all angles marked with a red square are $90^\circ$ and all angles marked with one black curve are equal, find the measure of the angle with a question mark.

Solution

It is given that the right angles are $90$ degrees, and that all the angles in the two triangles are all equal. We can already infer that the black angles are all $60$ degrees, since they are equilateral triangles.

There are $360$ degrees in a whole circle. We are given two of the black curves, and a $90$ degree angle, in which all three of them add up to $210$ degrees.