Answer:
m∠2 = 78°
Explanation:
Given:
m∠2 = (18x + 6)°
m∠3 = (21x + 18)°
To find:
m∠2
From the diagram, m∠2 and m∠3 are the same side interior angles. Same-side interior angles sum up to 180 degrees as they are supplementary angles. As a result,
m∠2 + m∠3 = 180°
(18x + 6)° + (21x + 18)° = 180°
[tex]\begin{gathered} 18x\text{ + 6 + 21x + 18 = 180} \\ 39x\text{ + 24 = 180} \\ \\ subtract\text{ 24 from both sides:} \\ 39x\text{ = 180 - 24} \\ 39x\text{ = 156} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 39:} \\ \frac{39x}{39}\text{ = }\frac{156}{39} \\ \\ x\text{ = 4} \end{gathered}[/tex][tex]\begin{gathered} m∠2\text{ = 18\lparen4\rparen + 6} \\ \\ m∠2\text{ = 78\degree} \end{gathered}[/tex]
