Question

Given: PKHE - inscribed, m∠E=120°
m∠EPK=51°, PF ∥EH
Find: m∠KPF, m∠H.

Answer 1

KPF = 9 and H = 129

Explanation:

An inscribed quadrilateral in a circle has all diagonal angles add up to 180, so we can use this to find the angles of the quadrilateral.

H= 180-EPK and K = 180-E so H = 129 and K = 60

Now PF and EH are parallel, so PE is a transversal. That means FPE = 180 - E = 60. Now it's pretty easy to solve for KPF = FPE - EPK = 60 - 51 = 9.

Let me know if you don't see how I did any of this and I'll be happy to explain it..