Question

In the diagram below, quadrilateral E, F, G, HEFGH is inscribed in circle II. Solve for x and y
I
E
F
G
H
60°
106°
(6y -60)°
(2x -98)°
Answer
Attempt 1 out of 2

x =
  y =

Answer 1

Because EFGH is cyclic, opposite angles are supplementary.

So pair the opposite angles:
- 60° + (6y − 60)° = 180° → 6y = 180 → y = 30
- 106° + (2x − 98)° = 180° → 2x + 8 = 180 → 2x = 172 → x = 86

Answer:
x = 86, y = 30