Question

<img src="https://gtm-media.discoveryeducation.com/videos/mathtechbook/images/medium/G8U06_C2O2_Q001_Image01.gif"

Consider the intersecting lines shown.If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

jigglypuff314 · Answer

Hi @Bubbly !

This problem has to do with the idea of Vertical Angles and Linear Angles

have you heard of these words before?

Bubbly · Answer

yes

Bubbly · Answer

but I don't really get it

jigglypuff314 · Answer

Great! well at least you've heard of them :)

It's ok if you don't understand them, lots of people don't

The ideas consist of:
If two angles are "vertical angles" then they are equal to each other.
and
If two angles are "linear angles" then they add up to 180 degrees

jigglypuff314 · Answer

Since we're only given the value of "m∠a=47°"
let's compare the rest of the angles to ∠a

is ∠b a vertical angle or a linear angle compared to ∠a ?

jigglypuff314 · Answer

|dw:1566409288673:dw|

Bubbly · Answer

Oh, okay

Bubbly · Answer

So b and d are vertical

jigglypuff314 · Answer

exactly :)

Bubbly · Answer

and a and c are linear? So are they all 47

jigglypuff314 · Answer

not quite!

b and d are vertical because they are opposite of each other right?

then by the same logic, a and c are also vertical angles

jigglypuff314 · Answer

however, the linear idea comes where the two angles are next to each other

like a and b are linear angles because they are next to each other

Bubbly · Answer

oh, okay. So how do I find what the missing measures are?

jigglypuff314 · Answer

if a and b are linear angles, then that means that they add up to 180 degrees

jigglypuff314 · Answer

we know that a = 47 degrees

so how might we find b?

Bubbly · Answer

180-47?

jigglypuff314 · Answer

perfect! that's exactly right :)

jigglypuff314 · Answer

we also know that a and c are vertical angles, which means that they are equal

so what would be the degree of c?

Bubbly · Answer

um, I'm going to take a guess and say 47

jigglypuff314 · Answer

that's a fantastic guess because you are correct ;D
you've got great intuition :)

then all is left is to find what d equals

Bubbly · Answer

okay so i'm guessing that d is also vertical, so I will say d=133 like b

jigglypuff314 · Answer

You're exactly right! :D

Bubbly · Answer

so b and d=133, and a and c=47

jigglypuff314 · Answer

yup! so that'll be your answer for this question ^_^

Bubbly · Answer

thank you so much for taking the time to take me through this problem, I have a much better understanding! 😊

jigglypuff314 · Answer

I'm really glad I could help :) Feel free to tag me with @jigglypuff314 if you need any more help and I happen to be online ^_^

Bubbly · Answer

okay, thanks have a great day