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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 23 Page 746

The Inscribed Angle Theorem says that the measure of an inscribed angle is half the measure of its intercepted arc. One of its corollaries says that an angle inscribed in a semicircle is a right angle.

30

Practice makes perfect

Consider the given diagram.

We want to find the value of x. The Inscribed Angle Theorem says that the measure of an inscribed angle is half the measure of its intercepted arc. One of its corollaries says that an angle inscribed in a semicircle is a right angle.

Since ∠ S is inscribed in a semicircle, we can say that it is a right angle. Recall that the sum of the interior angles of a triangle is 180^(∘). We can use it to write an equation for x. m∠ R + m∠ S + m∠ T = 180 ↓ x + 90 + 2x = 180 Let's solve it for x!

x + 90 + 2x = 180

Add and subtract terms

3x + 90 = 180

LHS-90=RHS-90

3x = 90

.LHS /3.=.RHS /3.

x = 30

Subchapter links

Exercises p.745-748