   Chapter 6.CT, Problem 1CT Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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 ⌢ = _____________. To determine

(a)

To find:

The measure of mACB=

Solution:

mACB=272°.

Explanation

Given:

mAB=88°

Approach:

The degree measured around a circle is 360°.

Calculation: 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.

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: 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. 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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