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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Review

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Exercise 14 Page 815

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

a=80, b=40, c=40, d=100

Practice makes perfect

Consider the given diagram.

Let's find the values of a, b, c, and d 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 40^(∘) — intercepts the arc that measures a^(∘), we can say that 40 is half of a. 40=a/2 ⇔ a=80

Thus, the value of a is 80.

Finding b

Remember that when parallel lines get crossed by a transversal, we can see that alternate interior angles are the same.

Since the angles with 40^(∘) and b^(∘) are alternate interior angles, they have the same measure, b=40.

Finding c

One of the corollaries to the Inscribed Angle Theorem says that two inscribed angles that intercept the same arc are congruent.

Therefore, since both inscribed angles in our diagram intercept the same arc, they are congruent. This means that they have the same measure, c=40.

Finding d

The sum of interior angles of a triangle is 180^(∘). Using this fact, we can find the value of d.

Let's substitute each b and c with 40 that we found earlier, and add the interior angle measures of our triangle.

d+40+40=180 ⇔ d=100

Thus, the value of d is 100.