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 2:

( mangle eba = mangle3 + 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 a point lies in the interior of an angle, the measure of the whole angle is equal to the sum of the measures of the two smaller angles. In this case, \(\angle EBA\) is composed of \(\angle 2\) and \(\angle 3\), so \(m\angle EBA=m\angle 3 + m\angle 2\) is based on the Angle Addition Postulate.

Answer:

D. Angle Addition Postulate