Question

Given that IHJ is equiangular, find x and y.

Answer 1

hint : equiangular => each angle = 60

Answer 2

This is a pretty cool problem.
As ganeshie8 said, if a triangle is equiangular, all angles must equal 60. Look at angle <KJL, which measures 57. Since HL is a straight line, the total angle must be 180.
We have 60 + 57 + x = 180.
Solve for x to get one angle of the middle triangle.

Answer 3

@bloopman thank you ! :)

Answer 4

That's not the x/y YOU want, though. If you can solve for x in that equation we can continue the problem

Answer 5

x=63

Answer 6

We know that JK is congruent to IK. Therefore, <IJK must be congruent to <JIK. To find the last angle of the triangle we solve:
2*63 + a = 180