Question

Help?


In the diagram, if m angle 2=150 degrees, then find the following...


m angle 1=
m angle 3=
m angle 4=

So, m angle 4=150 degrees as well because it's congruent to m angle 2. M angle 1 and m angle 3 should be the same because they're also congruent...right?

Answer 1

Why are those pairs of angles congruent?

Answer 2

They're congruent by the Vertical Angles Congruence Theorem

Answer 3

Right. Can you prove that theorem? Why is it true?

Answer 4

Okay well angle 1 and angle 3 are vertical angles and angle 1 and angle 4 are a linear pair, as well as angle 4 and 3. Angle 1 and angle 4 are also supplementary and so is angle 4 and 3. So I think by Congruent Supplements Theorem, angle 1 and angle 3 are congruent. (I have no idea if I did that right.)

Answer 5

That's the gist of it yeah, so angles 1 and 4 are supplementary, huh?

Answer 6

Yeah, I think

Answer 7

They form a linear pair, so that makes sense.
So what does that mean?

Answer 8

uh....the sum of their measures is 180 degrees?

Answer 9

Yep. I think you have everything you need to solve this problem now.

Answer 10

Um, you sure?

Answer 11

Definitely.

Answer 12

Just put it all together.

Answer 13

So how do I work it out with everything? I'm so confused. I'm sorry :/

Answer 14

You gave me a proof of why angles 2 and 4 are congruent and why angles 1 and 3 are congruent.
In that proof you mentioned that angles 1 and 4 are supplementary, and that that means they add up to 180º
If angle 4= angle 2, then what is angle 1?

Answer 15

Did you figure it out then @cerabear ?