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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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a) If m A B = 88 ° , then m A C B = ____________.

b) If m A B = 92 ° and C is the midpoint of major are ACB, then m A C = _____________.

Chapter 6.CT, Problem 1CT, a If mAB=88, then mACB=____________. b If mAB=92 and C is the midpoint of major are ACB, then

To determine

(a)

To find:

The measure of mACB=

Answer

Solution:

mACB=272°.

Explanation

Given:

mAB=88°

Approach:

The degree measured around a circle is 360°.

Calculation:

Elementary Geometry for College Students, Chapter 6.CT, Problem 1CT , additional homework tip  1

From the above circle we have,

mACB+mAB=360°mACB+88°=360°mACB=360°88°mACB=272°

To determine

(b)

To find:

The measure of mAC.

Answer

Solution:

mAC=134°.

Explanation

Given:

mAB=92°.

C is the midpoint of major are ACB.

Approach:

The degree measured around a circle is 360°.

Calculation:

Elementary Geometry for College Students, Chapter 6.CT, Problem 1CT , additional homework tip  2

From the above circle we have,

mACB+mAB=360°mACB+92°=360°mACB=360°92°mACB=268°

Now to find the measure of mAC.

It is given that C is the midpoint of major are ACB.

Elementary Geometry for College Students, Chapter 6.CT, Problem 1CT , additional homework tip  3

C is the midpoint of the arc ACB, then it cuts the arc into two congruent parts.

Thus, measure of the arc is mAC=mACB2.

mAC=2682mAC=134°

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