Skip over navigation
The interior angles are shown coloured in the diagram on the right.
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 $108^\circ$.
Stacking Shapes
Age 11 to 14
ShortChallenge Level 
The interior angles are shown coloured in the diagram on the right.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 $108^\circ$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
You may also like
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Days and Dates
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...