# Stacking Shapes

Weekly Problem 28 - 2017

The diagram on the right shows an equilateral triangle, a square and a regular pentagon. What is the sum of the interior angles of the resulting polygon?

The diagram on the right shows an equilateral triangle, a square and a regular pentagon. What is the sum of the interior angles of the resulting polygon?

## Problem

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What is the sum of the interior angles of the resulting polygon?

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

## Student Solutions

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The three blue angles are the interior angles of a triangle, so add up to $180^\circ$.

The four red angles are the interior angles of a square, which is a type of quadrilateral, so add up to $360^\circ$.

The five green angles are the interior angles of a pentagon, so add up to $540^\circ$.

Therefore, the total interior angle is $180^\circ + 360^\circ + 540^\circ = 1080^\circ$.

Since the shapes are regular, the angles could be individually counted. The blue angles are all $60^\circ$, the red angles are all $90^\circ$ and the green angles are all $108^\circ$.