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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Inscribed Angles

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Exercise 18 Page 746

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

34

Practice makes perfect

Consider the given diagram.

We want to find m∠ S. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Since both inscribed angles T and S — which measure (6x-2)^(∘) and (5x+4)^(∘) respectively — intercept the same RQ, we can say that (6x-2) is equal to (5x+4). Let's solve it for x.

(6x-2) = (5x+4)

Remove parentheses

6x - 2 = 5x + 4

LHS-5x=RHS-5x

x - 2 = 4

LHS+2=RHS+2

x = 6

Finally, we can evaluate m∠ S.

m∠ S = 5x + 4

x= 6

m∠ S = 5( 6) + 4

Multiply

m∠ S = 30 + 4

Add terms

m∠ S = 34^(∘)

Subchapter links

Exercises p.745-748