Question

I need explanations and help!

Answer 1

http://www.mathsisfun.com/geometry/alternate-interior-angles.html check there who's alternate interior or exterior or corresponding or vertical angles

and match against your picture

Answer 2

I figured out the alternate interior angles are <4 and <5, <3 and <6, <8 and <9, <7 and <10 am I correct?

Answer 3

yeap

Answer 4

Okay. What about same-side angles? match it against my picture?

Answer 5

same side interior would be the same as "consecutive interior angles"

thus

Answer 6

so that'd be
7 and 9
8 and 10
4 and 6
3 and 5

Answer 7

Okay good, that's what I got.

Answer 8

if line l is parallel to line m or l || m
then those angles equal each other

so you're given one of them.... say in part 3
5 = 80 so what's 2?
well 2 is the "corresponding angle" of 5 thus < 2 = <5

Answer 9

Okay, I knew they were parallel. Wouldn't it equal 80 degrees as well? Since it is parallel.

Answer 10

<5 = <2 since <5 = 80 thus yes, <2 = 80

Answer 11

Okay same for #4?

Answer 12

yeap for <3 is the "alternate interior" of <6 and thus <3 = <6

Answer 13

So, 110 degrees?

Answer 14

yes

Answer 15

For #5 would I plug in each answer and see which one fits best?

Answer 16

and also notice that < 2 is the "vertical angle" of <4
thus <2 = <4 thus \(\large {
\begin{cases}
\measuredangle 4\implies 12x+5\\
\measuredangle 5 \implies 8x+17\impliedby \measuredangle 2\\
thus\\
\measuredangle 4 \iff \measuredangle 2\impliedby vertical\ angles\\
thus\\
12x+5=8x+17
\end{cases}
}\)

solve for "x" see what you get.... and then plug back in 8x+17 to see what <2 is

Answer 17

Okay, it will take me a sec to solve.

Answer 18

k