SOLUTION: Hi, i'm not sure how to figure this question out. Could you please help? ABC is an equilateral triangle and BCDE is a square, find x. Diagram: http://imgur.com/a/2fhtn Thank

Algebra ->  Triangles -> SOLUTION: Hi, i'm not sure how to figure this question out. Could you please help? ABC is an equilateral triangle and BCDE is a square, find x. Diagram: http://imgur.com/a/2fhtn Thank      Log On


   

Question 1055746: Hi, i'm not sure how to figure this question out. Could you please help?
ABC is an equilateral triangle and BCDE is a square, find x.
Diagram: http://imgur.com/a/2fhtn
Thanks!
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Key is The isosceles triangle ABE. Side AB is congruent to side BE. The angle at B, on interior, is 90+60=150 degrees.

Upper interior angle at A is 60 degrees, but let this be the sum of your x plus y.
x%2By=60.

Now back to the isosceles triangle ABE. The TWO base angles each are of measure y.
You already know the 150 degrees at B.
2y%2B150=180
2y=30
highlight%28y=15%29

Now ready to find x.
Again, because equilateral, same as equiangular triangle,
x%2By=60
x=60-x
x=60-15
highlight%28x=45%29