Question

The parallel lines are marked with "feathers". Find the measures of the angles located at positions a, b, c, d, e, & f.

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Answer 1

Hi @shayy !

That's a lot of letters to look for but let's do this together step by step

Answer 2

The angle "a" and the 70 degree angle across from it are Vertical Angles

what do you know about vertical angles?

Answer 3

Their congruent

Answer 4

perfect! so what is angle A equal to?

Answer 5

70

Answer 6

awesome, you got it :)

let's go look at angle B next

angle B and the 135 degree angle make a "Linear Pair"
linear pairs will add up to equal 180 degrees

Answer 7

what do you think is the measure of angle B if this is the case?

Answer 8

45

Answer 9

perfect once again! :)

alright, the top is a little crowded but we can still go one by one

angle D and angle B are considered "alternate interior angles"

Answer 10

alternate interior angles will be equal to each other if we have parallel lines like we do in this problem

so what would angle D be equal to?

Answer 11

It be congruent

Answer 12

yes!
and since we found out before that angle B = 45 degrees

then what is angle D = ?

Answer 13

65

Answer 14

typo?

Answer 15

Is that correct

Answer 16

no, angle D would not be 65 degrees


angle D should be congruent to angle B
and we said that angle B was 45 degrees right?

Answer 17

Yes it would be congruent

Answer 18

yes so angle D would also be 45 degrees right?

Answer 19

Yes

Answer 20

nice,

let's consider what happens with angle C

We can see that the angles A, B, and C are the interior angles of a triangle

we know that a triangle adds up to 180 degrees

if we found out that angle A = 70, angle B = 45

we can use this information to find angle C

Answer 21

I’m confused

Answer 22

70 + 45 + C = 180

Answer 23

It’s 65

Answer 24

you got it! :)

Answer 25

next,

angle A and angle E are alternate interior angles

Answer 26

we know that A is 70 degrees
so what is E = ?

Answer 27

70

Answer 28

amazing!

last one:
angle E and angle F are a linear pair
they should add up to be 180 degrees

Answer 29

110

Answer 30

That’s the last one

Answer 31

yup! :)

Answer 32

Thank you for helping me, I was stress out