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Inscribed Hexagon

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

As the sum of the angles in a triangle is 180° and all four angles in a rectangle are 90°, then sum of the two marked angles in the triangle 180° - 90° = 90°.
Each interior angle of a regular hexagon is 120° and the sum of the angles in a quadrilateral is 360°; hence the sum of the two marked angles in the quadrilateral is 360° - 90° - (360° - 120°) = 30°.
Hence the sum of the four marked angles is 90° + 30° = 120°.

This problem is taken from the UKMT Mathematical Challenges.