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

- anonymous

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

- jamiebookeater

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- anonymous

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- anonymous

@ZeHanz this one.

- ZeHanz

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

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- anonymous

Also in this one, would y = 60?

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- anonymous

Alright,

- ZeHanz

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

- anonymous

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

- ZeHanz

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

- anonymous

111 is the measure of ABC

- anonymous

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

- anonymous

which is c?

- ZeHanz

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

yeah I got 42.

- ZeHanz

That's right!

- anonymous

But why did you times 2 times each?

- anonymous

never mind I know why now.

- anonymous

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

- ZeHanz

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

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

- anonymous

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

- anonymous

Measure of DCA = 21 degrees it seems really small?

- ZeHanz

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

- anonymous

alright

- anonymous

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

- anonymous

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?

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- anonymous

- ZeHanz

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

- anonymous

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

- anonymous

- ZeHanz

a²+144=400, so a²=?

- anonymous

16?

- ZeHanz

a²=256, so a=16, right!

- anonymous

thank you!

- ZeHanz

yw!

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