Regular vertex
A square, regular pentagon and equilateral triangle share a vertex. What is the size of the other angle?
Age
11 to 14
Challenge level
Problem
Image
The diagram shows an equilateral triangle, a square and a regular pentagon which all share a common vertex. What is the value of θ?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
The interior angles of an equilateral triangle, square, regular pentagon are 60 °, 90 °, 108 ° respectively. The sum of the angles at a point is 360 °. So θ = 360 - (60 + 90 + 108) = 102 °.