Question

statement reason 1) ray bd bisects ∠abc 1) given 2) m∠abd = m∠dbc 2) definition of bisector 3) m∠abd = 8(x + 4) 3) given 4) m∠dbc = 64 4) given 5) 8(x + 4) = 64 5) substitution 6) 8x + 32 = 64 6) distributive property 7) 8x = 32 7) ? 8) x = 4 8) what geometric reason justifies the transition from statement 6 to statement 7? multiplication property of equality subtraction property of equality division property of equality addition property of equality

Explanation:

Step1: Analyze the equations

From \(8x + 32=64\) to \(8x = 32\), we subtract \(32\) from both sides.

Step2: Recall the property

The Subtraction Property of Equality states that if \(a=b\), then \(a - c=b - c\). Here \(a = 8x+32\), \(b = 64\), and \(c = 32\).

Answer:

Subtraction Property of Equality