Equilateral Pair
Weekly Problem 39 - 2016
In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?
Problem
In the diagram, $VWX$ and $XYZ$ are congruent equilateral triangles, and $\angle VXY$ is $80^{\circ}$.
What is the size of $\angle VWY$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Since $VXW$ is an equilateral triangle, $\angle VXW = 60^\circ$. Therefore $\angle WXY = \angle WXV + \angle VXY = 60^\circ + 80 ^ \circ = 140^\circ$.
Since the equilateral triangles are congruent, $WX = XY$, so the triangle $WXY$ is isosceles. Therefore, $\angle YWX = \angle XYW = \frac{1}{2}\left(180^\circ - \angle WXY\right) = \frac{1}{2}\left(180^\circ - 140^\circ\right) = 20^\circ$.
Then, since $VXW$ is equilateral, $\angle VWX = 60^\circ$. Then, $\angle VWY = \angle VWX - \angle YWX = 60^\circ - 20^\circ = 40^\circ$.