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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

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Exercise 7 Page 541

To find m∠ DBF we need to find the value of x first. Remember that the angle bisector always divides the angle into two equal parts. Also, the angle between opposite rays is a straight angle.

64.5

Practice makes perfect

Since BD bisects ∠ ABF and the angle bisector always divides the angle into two equal parts, we have that m∠ DBF= 12m∠ ABF.

Therefore, to find m∠ DBF we need to find the value of m∠ ABF first. We will use the given information. m∠ FBC &= 2x+25 m∠ ABF &= 10x-1We also know, that BA and BC are opposite rays, which means that the angle between them is a straight angle. Therefore, the sum of their measures is 180. m∠ FBC+m∠ ABF=180 Let's substitute the given values of m∠ FBC and m∠ ABF into the above equation, and solve for x.

m∠ FBC+m∠ ABF=180

m∠ FBC= 2x+25, m∠ ABF= 10x-1

2x+25+ 10x-1=180

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Solve for x

Add and subtract terms

12x+24=180

LHS-24=RHS-24

12x=156

.LHS /12.=.RHS /12.

x=13

Now, let's substitute 13 for x in m∠ ABF=10x-1.

m∠ ABF=10x-1

x= 13

m∠ ABF=10( 13)-1

Multiply

m∠ ABF=130-1

Subtract term

m∠ ABF=129

Finally, recall that AD bisects ∠ ABF. Therefore, to find m∠ DBF, we will multiply m∠ DBF by 12.

m∠ DBF=1/2m∠ ABF

m∠ ABF= 129

m∠ DBF=1/2( 129)

MoveRightFacToNumOne

1/b* a = a/b

m∠ DBF=129/2

Calculate quotient

m∠ DBF=64.5

We found that m∠ DBF=64.5.

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