Question

(b) problem 12: (first taught in lesson 16)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: m∠rst + m∠2 = 180 and m∠2 + m∠def = 180
prove: m∠rst = m∠def
a b c d e
if two angles are complementary to the same angle, then they are equal.

Explanation:

Step1: Analyze given equations

We have \(m\angle RST + m\angle2=180\) and \(m\angle2 + m\angle DEF = 180\). This means \(\angle RST\) and \(\angle DEF\) are both supplementary to \(\angle2\).

Step2: Apply angle - property

The property that if two angles are supplementary to the same angle (in this case \(\angle2\)), then they are equal, justifies the prove statement \(m\angle RST=m\angle DEF\).

Answer:

A. If two angles are complementary to the same angle, then they are equal.