Question

statement reason 1) abc is a triangle 1) given 2) m∠a + m∠b + m∠c = 180° 2) triangle angle theorem 3) m∠a = 3x + 8 3) given 4) m∠b = 3x 4) given 5) m∠c = 3x + 10 5) given 6) 3x + 8 + 3x + 3x + 10 = 180 6) substitution 7) 9x + 18 = 180 7) algebra 8) 9x = 162 8) subtraction property of equality 9) x = 18 9) ? 10) m∠c = 3(18) + 10 10) 11) m∠c = 64° 11) algebra what geometric reason justifies the transition from statement 8 to statement 9? division property of equality substitution subtraction property of equality symmetric property

Explanation:

From statement 8 ($9x = 162$) to statement 9 ($x = 18$), we divide both sides of the equation by 9. The Division Property of Equality states that if $a = b$ and $c
eq0$, then $\frac{a}{c}=\frac{b}{c}$. Here, $a = 9x$, $b = 162$, and $c = 9$.

Answer:

Division Property of Equality