Question

statement reason

1. ray bd bisects \\( \angle abc \\) 1) given
2. \\( m\angle abd=m\angle dbc \\) 2) definition of bisector
3. \\( m\angle abd=8(x + 4) \\) 3) given
4. \\( m\angle dbc=64 \\) 4) given
5. \\( 8(x + 4)=64 \\) 5) substitution
6. \\( 8x + 32=64 \\) 6) distributive property
7. \\( 8x=32 \\) 7) subtraction property of

equality

1. \\( x = 4 \\) 8) ?

what geometric reason justifies the transition
from statement 7 to statement 8?
division property of equality
multiplication property of equality
addition property of equality
subtraction property of equality

Explanation:

From statement 7 ($8x = 32$) to statement 8 ($x = 4$), we divide both sides of the equation $8x = 32$ by 8. According to the Division Property of Equality, if $a=b$ and $c
eq0$, then $\frac{a}{c}=\frac{b}{c}$. Here $a = 8x$, $b = 32$, and $c = 8$. So the Division Property of Equality justifies this transition.

Answer:

A. Division Property of Equality