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?
Age
11 to 14
Challenge level
Problem
The diagram shows three squares drawn on the sides of a triangle. What is the sum of the three marked angles?
Image
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 °.