   Chapter 6.CR, Problem 8CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Review Exercises 5 to 10, B A → is tangent to the circle at point A in the figure shown. m ∠ D = 40 ° ,   m D C ^ = 130 ° ,     m ∠ B = ? To determine

To find: mB

Explanation

Theorem:

1) The measure of an angle formed when two secants intersect at a point outside the circle is one-half the difference of the measures of two intercepted arcs.

2) The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Calculation:

Given that

mD=40°, mDC^=130° and BA is tangent to the circle at point A.

By theorem, The measure of an inscribed angle ADC of a circle is one-half the measure of its intercepted arc mAC^.

40°=12mAC^

40°×2=12mAC^×2

80°=mAC^

Therefore, mAC^=80°

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