Exercise 14 Page 749

An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, in the given diagram ∠ E and ∠ F are inscribed angles. The arc HG is the corresponding intercepted arc.

Let's recall Theorem 10.7.

Since ∠ E and ∠ F intercept the same arc they are congruent. By the definition of congruence the angles have the same measure. ∠ E ≅ ∠ F ⇓ 8x+6= 10x-4 Let's solve this equation.

This matches answer G.