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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 14 Page 749

What can be said of two inscribed angles of a circle that intercept the same arc?

G

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.

A circle with two inscribed angles that intercepts the same arc.

Let's recall Theorem 10.7.

Theorem 10.7
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

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.

8x+6=10x-4

▼

Solve for x

LHS-6=RHS-6

8x=10x-10

LHS-10x=RHS-10x

- 2x=- 10

.LHS /- 2.=.RHS /- 2.

x=5

This matches answer G.

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