   Chapter 1.4, Problem 45E ### 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
1 views

# On the hanging sign, the three angles ( ∠ A B D , ∠ A B C ,   and   ∠ D B C   ) at vertex B have the sum of measures 360 ° . If m ∠ D B C = 90 ° and B A → bisects the indicated reflex angle, find m ∠ A B C . To determine

To find:

The measure of the ABC.

Explanation

Given:

The three angles ABD, ABC and DBC have the sum of measures 360°.

The measure of DBC is 90° and BA bisects the indicated reflex angle.

The given figure is,

Definition:

The bisector separates an angle into two congruent angles.

Approach:

Consider the figure,

BA bisects the reflex angle DBC into two congruent angles that gives,

mABC=mABD

It is given the three angles ABD, ABC and DBC have the sum of measures 360°.and the measure of DBC is 90°

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