Exercise 7 Page 749

The Arc Addition Postulate tells us that the measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

In the given diagram we want to find the measure of the arc BC.

Note that the BB' is a diameter, and also that BC and CB' are adjacent arcs. Let's recall the Arc Addition Postulate.

Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs.

In this case, the arc formed by these two adjacent arcs is a diameter and has an arc measure of 180. mBC+mCB'=180^(∘) According to the diagram mCB'= 168^(∘). Let's substitute this value in the above equation and solve for mBC.

mBC+mCB'=180

Substitute

mCB'= 168

mBC+ 168=180

SubEqn

LHS-168=RHS-168

mBC= 12

We found that BC measures 12^(∘). Let's recall the formula for finding the length of an arc.

We know that the circle's diameter is 21 cm. To find the radius we can divide the diameter by 2. r=21/2= 11.5 Let's substitute 12 for θ and 11.5 for r in the formula to find the arc length.

l=θ/360^(∘)* 2π r

SubstituteII

θ= 12, r= 11.5

l=12/360^(∘)* 2π ( 11.5)

UseCalc

Use a calculator

l=2.19911...

RoundDec

Round to 2 decimal place(s)

l≈ 2.20

The length of the arc rounded to the nearest hundredth is 2.20 cm, which matches answer B.

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Exercise 7 Page 749

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