Question

Part A: Which relationship describes <1 and <2? Part B: What is the value of x?Part C: What is the m<2?

Answer 1

`\begin{gathered} a)Alternate\: Exterior\: Angles \\ b)x=8 \\ c)71^(\circ) \end{gathered}`

1) Consider that there is a pair of parallel lines intercepted by a transversal one. Therefore, the rules of parallelism are valid.

a) Examining ∠1 and ∠2 we can see that these angles are Alternate Exterior Angles and they are congruent to each other.

b) Once we know they are congruent to each other we can equate the measure of their angles given in these expressions. And then we can solve for x;

`\begin{gathered} 7x+15=10x-9 \\ 7x+15-15=10x-9-15 \\ 7x=10x-24 \\ 7x-10x=10x-10x-24 \\ -3x=-24 \\ (-3x)/(-3)=(-24)/(-3) \\ x=8 \end{gathered}`

c) Now, we can plug into any of those equations the value of x:

`\begin{gathered} m\angle2=10x-9 \\ m\angle2=10(8)-9 \\ m\angle2=80-9 \\ m\angle2=71 \end{gathered}`