Question

If AB is parallel to CD, angle A = 35 degrees and angle C = 45 degrees, find the number of degrees in angle AEC.

Answer 1

could you help me?

Answer 2

I'd start with extending CE until it intersects AB
and extending AE until it intersects CD

Answer 3

Does that give you a clue?

Answer 4

ah....

Answer 5

ah...? you get it? :)

Answer 6

ahhh....

Answer 7

could you give me another hint?

Answer 8

70 degrees

draw a line parallel to AB through E and use "alternate interior angles are same"

Answer 9

hmm

Answer 10

70 degrees...

Answer 11

I'm thinking @ganeshie8 's method is more efficient, I'll let him do the rest

Answer 12

teren's method is much simpler. try it once..

Answer 13

alternate interior angles and vertical angles equal one another.

Answer 14

I know that.

Answer 15

but...

Answer 16

I'm used to the ol' transversal thing

Answer 17

with the two straight lines and third one intersecting the two.

Answer 18

Ok, uhh, if you extend CE until it intersects AB,
And let's call their point of intersection F
you with me?

Answer 19

yep

Answer 20

now I see that part

Answer 21

ok, then what would be the measurement of the angle EFA?

Answer 22

umm...

Answer 23

you said 70 degrees, right?

Answer 24

I didn't, gan did I don't know what answer we'll come up with :P

Answer 25

hmm...

Answer 26

so, back to our setup
what's the measurement of angle EFA?

Answer 27

well...

Answer 28

45 degrees?

Answer 29

alternate exterior angles are equal?

Answer 30

actually, they're alternate interior angles ;)

Answer 31

k

Answer 32

so 45 degrees?

Answer 33

so, a triangle is formed
Angle A is 35
Angle EFA is 45
What must be the measurement of angle AEF?

Answer 34

lol 100

Answer 35

180 rule

Answer 36

that's right
And angle AEC forms a linear pair with that angle, so
AEC must measure up to....?

Answer 37

80!!

Answer 38

And gan got 70
you want me to show you where he made an error?

Answer 39

80+100=180

Answer 40

But how he did he get 70? do you know?

Answer 41

that's a fundamental rule, right?

Answer 42

he did not follow the rule of 180?

Answer 43

or he did not choose to make a triangle?

Answer 44

actually, there was an easier way of getting AEC, :) it starts off like gan did

Answer 45

so, you draw a line through E that is parallel to AB

Answer 46

get me so far?

Answer 47

k

Answer 48

That new line must be parallel to both AB and CD right?

Answer 49

yes.1

Answer 50

I mean yes

Answer 51

So, let's call that line FG, with F to the left of E and G to the right of E
get it so far?

Answer 52

yes

Answer 53

ok, A is 35 degrees, so, angle AEF, being its alternate interior, must also be 35 degrees right?

Answer 54

alternate interior angles are the same.

Answer 55

thats a fundamental rule

Answer 56

Yes, so AEF is 35 degrees
Now,
C is 45 degrees
so CEF, being its alternate interior, must also be 45 degrees, right?

Answer 57

yes

Answer 58

it has to abide by the rules

Answer 59

Well, the measure of AEC must be the sum of the measures of AEF (35) and CEF (45) which is...? :)

Answer 60

80!!!!!!!!!!!!

Answer 61

et voila

Answer 62

k

Answer 63

I'm going to post one more geometry problem

Answer 64

keep me posted :)