# Outside the Boxes

Weekly Problem 13 - 2008

The diagram shows three squares drawn on the sides of a triangle. What is the sum of the three marked angles?

The diagram shows three squares drawn on the sides of a triangle. What is the sum of the three marked angles?

## Problem

The diagram shows three squares drawn on the sides of a triangle. What is the sum of the three marked angles?

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If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

At each vertex of the triangle, four angles meet which must add up to 360 °. Therefore altogether the twelve angles add up to 3 x 360 °. Six of the angles are right-angles, and three of them are the internal angles of the triangle, which add up to 180 °.

So the sum of the remaining three angles must be (3 x 360 °) - (6 x 90 °) - 180 ° = 360 °.