What can you say about the sides of an equiangular triangle?
x=5
y^(∘)=20^(∘)
Practice makes perfect
Examining the diagram, we can spot two equiangular triangles which means all angles in these triangles have a measure of 60^(∘). Also, according to the Corollary to the Converse of the Base Angles Theorem, if a triangle is equiangular, then it is equilateral as well. Let's add this information to the diagram.
Therefore, the sides marked as 5x-1 and 24 are congruent. This means we can equate their measures and solve for x.
To solve for y, we have to consider the fact that 60^(∘) and 6y form a linear pair. By the Linear Pair Postulate we know these angles are supplementary. Therefore, we can equate their sum with 180^(∘) and solve for y.
