A B -------------- E --- C ------- D (Since, I cannot attach

Question

------- A

B -------------- E

 --- C ------- D

(Since, I cannot attach a jpg, connect the pts ABCDE to form a pentagon.)

In the figure, What is the measure of angle ACB?

1) Triangle ACD is an equilateral triangle.
2) AB=BC=AE=DE

rxs0005 · Answer

I would have to go with C 

As I would be the inner triangle is 60-60-60 but we cannot make out about ACB 

from II nothign can be said 

from I and II all sidesof the traingle become equal so it will be 60 deg

gayathri · Answer

How do you get all sides are equal?
1) gives you AC=AD=CD
2) gives you AB=BC=AE=DE

How do you combine the two?

twixt · Answer

I pick C as statement 2 is not enough.

vprabhala · Answer

I would go with E. how is it C? guys please explain..

gayathri · Answer

Twixt can you explain your approach?

mallelac · Answer

I am getting it as E. I may not be able to explain at length here because of the diagrams. However, both the stems either individually or together are not giving us any conclusice stuff. so, E..I am eager to know the answer 8-)

vprabhala · Answer

can you explain how you are getting C

mallelac · Answer

The stem is asking ACB angle but not ACD. Only ACD can be 60 degrees.

twixt · Answer

All sides are not equal actually...
If they were, pentagon would become an hexagon...

twixt · Answer

There is no conclusion from statement 1 neither from statement 2.

Both together : considering that 0 is the circle center then OA=OC=OB
then ACB=ACO

As ACD is equilateral O must be the barycenter (?) of the triangle and in this specific case line CO divides equally the angle C
So ACO=ACB = 30 degrees to me.

twixt · Answer

There is no conclusion from statement 1 neither from statement 2.

Both together : considering that 0 is the circle center then OA=OC=OB
then ACB=ACO

As ACD is equilateral O must be the barycenter (?) of the triangle and in this specific case line CO divides equally the angle C
So ACO=ACB = 30 degrees to me.

gayathri · Answer

OA is E 

Twixt, from your explanation it looks like you are assuming that the pentagon is a regular pentagon (OA=OC=OB). But we do not know that.

rxs0005 · Answer

I think i know what mistake i made

 i did not read the Q properly i assumed 

CD was = too in the II statement since CD is common to ACD and CA common to CBA 
i concluded that both ABC and ACD are equilateral Triangle

good Q G!

twixt · Answer

My mistake gayathri, I do not know why I was thinking all your points were standing on a circle... :oops:

If not E is clear

banerjeea_98 · Answer

Hmmm...i made the assumption of regular pentagon....my bad, in that case "E" is correct.

A B -------------- E --- C ------- D (Since, I cannot attach

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