Question

use the information shown here to complete the proof. given each statement, provide the correct reason.
given: ( mangle1 = mangle3 )
prove: ( mangle eba = mangle dbc )

1. statement 3:

( mangle eba = mangle1 + mangle2 )
a. substitution property of equality
b. given
c. division property of equality
d. angle addition postulate

Explanation:

The Angle Addition Postulate states that if we have two adjacent angles, the measure of the larger angle formed is the sum of the measures of the two smaller adjacent angles. In this case, \(\angle EBA\) is composed of \(\angle1\) and \(\angle2\), so \(m\angle EBA=m\angle1 + m\angle2\) is based on the Angle Addition Postulate.

Answer:

D. Angle Addition Postulate