Question

http://oi49.tinypic.com/35m2sxt.jpg

G is the incenter of Δ ABC.
m∠A = 58
m∠B = 64
m∠C = 58

What is the m∠BCE?

36

27

32

29

Answer 1

incenter: constructed by angle bisectors
In other words, ∠ BCE = ∠ ACE
From the given information, m∠C = 58
and ∠ BCE + ∠ ACE = ∠C
So, 2 ∠BCE = ∠C
2 ∠BCE = 58
Time to solve it.

Answer 2

its 32?

Answer 3

@Callisto

Answer 4

How did you get that?

Answer 5

Oh no,i solved it wrong,Omg i dont get it.

Answer 6

Which part??

Answer 7

I dont get how∠BCE = ∠C.. From wat i think it should be 27 right?

Answer 8

I recommend you stop guessing...
Do you understand ∠ BCE + ∠ ACE = ∠C?

Answer 9

no i dont..

Answer 10

Can you look at the figure you posted again? Can you see that ∠ BCE + ∠ ACE = ∠C ...

Answer 11

Yeah!

Answer 12

So, I assume you get how come ∠ BCE + ∠ ACE = ∠C...

Now, by definition of incentre, incenter is constructed by angle bisectors of the 3 angles in a triangle.
Consider angle C, ∠ BCE = ∠ ACE
Got it so far?

Answer 13

Yeah,thanx!

Answer 14

I still dont get how to get the answer though

Answer 15

Because I haven't finished :|

Conditions you have:
(1) ∠ BCE = ∠ ACE
(2) ∠ BCE + ∠ ACE = ∠C
(3) ∠C = 58

Sub. (1) and (3) into (2)
∠ BCE + ∠ BCE = 58

Now can you solve it?

Answer 16

im solving it right now

Answer 17

Hint: ∠ BCE + ∠ BCE = 2 ∠ BCE

Answer 18

I got 29!

Answer 19

Yup :)

Answer 20

Do you know how to do it now??

Answer 21

Yeah,Thank you!

Answer 22

Welcome :)