Geometric quadrilateral
Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?
Age
11 to 14
Challenge level
Problem
Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one.
What is the size of the smallest interior angle?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $24^\circ$
Image
The angles in a quadrilateral add up to $360^\circ$, so this tells us that:$$x+2x+4x+8x = 360^\circ$$ Collecting like terms gives:$$15x = 360^\circ$$ Dividing by $15$ gives:$$x = 24^\circ$$ Therefore, the smallest angle in the quadrilateral is $24^\circ$.