   Chapter 1.CR, Problem 20CR ### 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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# Given: B D → bisects ∠ A B C m ∠ A B D = 2 x + 15 m ∠ D B C = 3 x + 5 Find: m ∠ A B C To determine

To find:

The value of mABC.

Explanation

Given:

mABD=2x+15

mDBC=3x+5

And,

BD bisects ABC.

The Figure (1) is given as,

Figure (1)

Approach:

The bisector of an angle is the ray that separates the given angle into two congruent angles.

Calculation:

Since, BD is bisecting the angle ABC then it can be written as,

mABD=mDBC(1)

mABC=2×mABD(2)

Substitute 2x+15 for mABD and 3x+5 for mDBC in the above equation (1).

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