lines b and c are parallel. what is the measure of ∠6? m∠6 = 45° m∠6 = 54° m∠6 = 117° m∠6 = 126°

lines b and c are parallel. what is the measure of ∠6? m∠6 = 45° m∠6 = 54° m∠6 = 117° m∠6 = 126°

lines b and c are parallel. what is the measure of ∠6? m∠6 = 45° m∠6 = 54° m∠6 = 117° m∠6 = 126°

Answer

Explanation:

Step1: Use the property of same - side interior angles

Since lines (b) and (c) are parallel, ((13x + 9)+(5x + 9)=180) (same - side interior angles are supplementary). [ \begin{align*} 13x+9 + 5x+9&=180\ 18x+18&=180\ 18x&=180 - 18\ 18x&=162\ x&=9 \end{align*} ]

Step2: Find the measure of (\angle6)

Substitute (x = 9) into (\angle6)'s adjacent angle ((5x + 9)) (5x+9=5\times9 + 9=45+9 = 54) Since (\angle6) and ((5x + 9)) are supplementary (linear pair), (m\angle6=180-(5x + 9)) Substitute (x = 9), (m\angle6=180 - 54=126^{\circ})

Answer:

(m\angle6 = 126^{\circ}) (the fourth option)