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

Question

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

anonymous · Answer

attachment

anonymous · Answer

@ZeHanz this one.

zehanz · Answer

OK, the incenter is the intersection of the angle bisectors.
You have two more angles now!

anonymous · Answer

Also in this one, would y = 60?

anonymous · Answer

Alright,

zehanz · Answer

y=60 degrees, if the triangle is supposed to be equilateral.

anonymous · Answer

alright , now for the other problem, how do you find the measure of angle DCA?

zehanz · Answer

Better question, what are the measures of the angles CAB and ABC?

anonymous · Answer

111 is the measure of ABC

anonymous · Answer

I meant they all equal 180. But the missing one is 111.

anonymous · Answer

which is c?

zehanz · Answer

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.

anonymous · Answer

yeah I got 42.

zehanz · Answer

That's right!

anonymous · Answer

But why did you times 2 times each?

anonymous · Answer

never mind I know why now.

anonymous · Answer

So the measure of angle DCA would be 32 + 42 + what?

zehanz · Answer

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...

zehanz · Answer

DC is bisector of the angle we just found: 42 degrees, so 21 degrees is the measure of DCA!

anonymous · Answer

But I thought the wanted the measure of the whole angle?

anonymous · Answer

Measure of DCA = 21 degrees it seems really small?

zehanz · Answer

I'll make a drawing, hold on...

anonymous · Answer

alright

anonymous · Answer

Im pretty sure I understand now. They just want the measure of C?

anonymous · Answer

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?

anonymous · Answer

@ZeHanz

zehanz · Answer

If there is a right angle in the triangle (there is!) then a²+12²=20².
You can work out a now.

anonymous · Answer

Yeah But I can't seem to get it? how to get a?

anonymous · Answer

@ZeHanz

zehanz · Answer

a²+144=400, so a²=?

anonymous · Answer

16?

zehanz · Answer

a²=256, so a=16, right!

anonymous · Answer

thank you!

zehanz · Answer

yw!