Problem finding exterior angle

[1/2"]

Homework Statement

Triangle ABC has been inscribed in the circle with center o.E is the midpoint of arc BC.DE is the diameter.E is joined to A, B and C.D is joined to A . If angle ABC =72 degrees and angle ACB = 48 degrees,
find angle DAC.
(I have attached the diagram given in book although its not a very good one)

Homework Equations

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The Attempt at a Solution

In this one what i did was,
i found angle BAC =(180-72-48)= 60 degrees
then i tried to subtend angle from the diameter to get 90 degree on the circumference but it did not help.
and i found the other angles like angle BEA=48 degrees and angle DEC= 72 degrees by the theorem the a chord extend equal angles on the circumference. But i can't get any further than this .Please help.
the answer given in my book is 60 degrees.
If I am going wrong somewhere please do let me know.
Thank you.

 

[tiny-tim]

hi 1/2"!

use the theorem that opposite angles subtended from the same chord (ie opposite angles of an inscribed quadrilateral) add up to 180°

 

[1/2"]

I think i have already done it.
can you please be alittle more elaborate?
thanks.

 

[tiny-tim]

I think i have already done it.
can you please be alittle more elaborate?
thanks.

i'm confused … if you've already done it, what's the problem?

and I've given you the full theorem … what is there to elaborate further?

 

[1/2"]

I am really sorry to confuse you.
Could you give a more direct clue how to get the angle DAC?
and i am really sorry.

 

[1/2"]

Thank you
but i have got it.