lines b and c are parallel. what is the measure of ∠2? m∠2 = 31° m∠2 = 50° m∠2 = 120° m∠2 = 130°
lines b and c are parallel. what is the measure of ∠2? m∠2 = 31° m∠2 = 50° m∠2 = 120° m∠2 = 130°
Answer
Explanation:
Step1: Use the property of adjacent angles
Since lines (b) and (c) are parallel, (\angle1=(7x + 1)^{\circ}) and (\angle2=(18x + 4)^{\circ}) are adjacent angles on a straight - line. So ((7x + 1)+(18x + 4)=180). $$ \begin{align*} 7x+1+18x + 4&=180\ 25x+5&=180\ 25x&=180 - 5\ 25x&=175\ x&=7 \end{align*} $$
Step2: Calculate the measure of (\angle2)
Substitute (x = 7) into (\angle2=(18x + 4)^{\circ}). Then (\angle2=(18\times7+4)^{\circ}=(126 + 4)^{\circ}=130^{\circ})
Answer:
(m\angle2 = 130^{\circ})