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Find the measure of angle DCA if D is the incenter of the triangle ABC. Explain step by step please!

Mathematics
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@ZeHanz this one.
OK, the incenter is the intersection of the angle bisectors. You have two more angles now!

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Other answers:

Also in this one, would y = 60?
Alright,
y=60 degrees, if the triangle is supposed to be equilateral.
alright , now for the other problem, how do you find the measure of angle DCA?
Better question, what are the measures of the angles CAB and ABC?
111 is the measure of ABC
I meant they all equal 180. But the missing one is 111.
which is c?
DOn't know how you get these numbers. Remember: the lines drawn to the incenter are the angle bisectors. That means: angle CAB = 2*32 = ... angle ABC = 2*37 = ... Add these and subtract from 180 to get angle ACB.
yeah I got 42.
That's right!
But why did you times 2 times each?
never mind I know why now.
So the measure of angle DCA would be 32 + 42 + what?
Look at the drawing. The numbers are the measures of half the angles, because the lines to the incenter are the: angle b i s e c t o r s...
DC is bisector of the angle we just found: 42 degrees, so 21 degrees is the measure of DCA!
But I thought the wanted the measure of the whole angle?
Measure of DCA = 21 degrees it seems really small?
I'll make a drawing, hold on...
alright
Im pretty sure I understand now. They just want the measure of C?
Also I know that a squared + b squared = c squared. But this triangles does not show any angles so except 90 degrees. So Im not sure how to find x?
If there is a right angle in the triangle (there is!) then a²+12²=20². You can work out a now.
Yeah But I can't seem to get it? how to get a?
a²+144=400, so a²=?
16?
a²=256, so a=16, right!
thank you!
yw!

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