Answer:
156.9
Explanation:
∠x=4(∠y)
Angles in a triangle add to 180:
∠x+∠y+90=180
4(∠y)+∠y=90
5(∠y)=90
∠y=18
The left side of the parallelogram is opposite ∠y, which we know, and we know the adjacent (marked as 57) so we can use tan:
tanA=opposite/adjacent
tan18=(side)/57
side=18.5204226853
Similarly, we can find the base of the shape using cos:
cosA=adjacent/hypotenuse
cos18=57/(base)
base=59.9333467816
Perimeter = 2(side)+2(base)
=2(18.5204226853)+2(59.9333467816)
=37.0408453706+119.866693563
=156.907538934
≈156.9