Question

I don't understand this question.

Answer 1

Well CD is an angle bisector of triangle ABC, but not too sure about BD

Answer 2

ohhh.

Answer 3

could be a typo maybe?

Answer 4

Hmm maybe. It doesn't look like an altitude becaue altitudes are straight?

Answer 5

If they really meant to write "CD" instead of "BD", then it's an angle bisector.

Answer 6

And then medians .....are errr.

Answer 7

No it's not an altitude because altitudes are perpendicular (ie make 90 degree angles) with the opposite side.

Answer 8

Ohhhh! okay

Answer 9

Not a median because its not cutting that opposite side in half

Answer 10

And it's not a perpendicular bisector because it's neither of the two listed above

Answer 11

Hmm..

Answer 12

So maybe an angle bisector?

Answer 13

yes, that's what I'm thinking as well

Answer 14

because the construction marks show us that we're cutting angle ACB in half

Answer 15

Alrighty! Thanks for helping me and explaining why it couldn't be the certain answers.
Do you mind if I ask you one more question?

Answer 16

sure go for it

Answer 17

okay this is one that i don't understand the process in which to do it.

Answer 18

would it be maybe like x+(5x+12)+(4x+2) = 180?

Answer 19

Is there a picture for this one?

Answer 20

Yes its the one above the one i just posted.

Answer 21

one.png.

Answer 22

in "one.png" though, it's just the problem without a picture

Answer 23

If you don't have a picture for this one, what is the relationship between A B and C? Do they form a triangle?

Answer 24

I GOT IT

Answer 25

thank you

Answer 26

no thank you!

Answer 27

By the angle addition postulate, we know that


m < ABD = m < ABE + m < EBD


m < ABD = x + (5x+12)


m < ABD = 6x + 12

-------------------------------------------------------

By the exterior angle theorem, we can say


m < C + m < D = m < ABD


m < C + (4x+2) = 6x+12


m < C = 6x+12-4x-2


m < C = 2x+10


So m < C = 2x + 10

=====================================================================

By the construction marks, we know that m < DBC = m < EBA = x


So m < DBC = x


and


m < DBC + m < C + m < D = 180


x + (2x+10) + (4x+2) = 180


7x+12 = 180


7x = 180-12


7x = 168


x = 168/7


x = 24


Now that we know that x = 24, we can use it to find m < C


m < C = 2x+10


m < C = 2*24+10


m < C = 48+10


m < C = 58



So the answer is choice D