body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

3. Inscribed Angles

Continue to next subchapter

Exercise 14 Page 784

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.

a = 50, b = 90, and c = 90

Practice makes perfect

Consider the given diagram.

Let's find the values of a, b, and c one at a time.

Finding a

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

Since the inscribed angle — which measures 25^(∘) — intercepts the arc that measures a^(∘), we can say that 25 is half of a.

25 = 1/2a

LHS * 2=RHS* 2

50 = a

Rearrange equation

a = 50

Finding b

One of the corollaries of the Inscribed Angle Theorem says that an angle inscribed in a semicircle is a right angle.

Since the angle whose measure is b^(∘) is inscribed in a semicircle, we can say that it is a right angle. Therefore, we have that b=90.

Finding c

Once again, recall that angle inscribed in a semicircle is a right angle.

Since the angle whose measure is c^(∘) is inscribed in a semicircle, we can say that it is a right angle. Therefore, we have that c=90.

Subchapter links

Lesson Check p.784

Practice and Problem-Solving Exercises p.784-787

Standardized Test Prep p.787

Mixed Review p.787