anonymous
  • anonymous
Find the measure of angle DCA if D is the incenter of the triangle ABC. Explain step by step please!
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
@ZeHanz this one.
ZeHanz
  • ZeHanz
OK, the incenter is the intersection of the angle bisectors. You have two more angles now!

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anonymous
  • anonymous
Also in this one, would y = 60?
anonymous
  • anonymous
Alright,
ZeHanz
  • ZeHanz
y=60 degrees, if the triangle is supposed to be equilateral.
anonymous
  • anonymous
alright , now for the other problem, how do you find the measure of angle DCA?
ZeHanz
  • ZeHanz
Better question, what are the measures of the angles CAB and ABC?
anonymous
  • anonymous
111 is the measure of ABC
anonymous
  • anonymous
I meant they all equal 180. But the missing one is 111.
anonymous
  • anonymous
which is c?
ZeHanz
  • 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
  • anonymous
yeah I got 42.
ZeHanz
  • ZeHanz
That's right!
anonymous
  • anonymous
But why did you times 2 times each?
anonymous
  • anonymous
never mind I know why now.
anonymous
  • anonymous
So the measure of angle DCA would be 32 + 42 + what?
ZeHanz
  • 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
  • ZeHanz
DC is bisector of the angle we just found: 42 degrees, so 21 degrees is the measure of DCA!
anonymous
  • anonymous
But I thought the wanted the measure of the whole angle?
anonymous
  • anonymous
Measure of DCA = 21 degrees it seems really small?
ZeHanz
  • ZeHanz
I'll make a drawing, hold on...
anonymous
  • anonymous
alright
anonymous
  • anonymous
Im pretty sure I understand now. They just want the measure of C?
anonymous
  • 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?
anonymous
  • anonymous
ZeHanz
  • ZeHanz
If there is a right angle in the triangle (there is!) then a²+12²=20². You can work out a now.
anonymous
  • anonymous
Yeah But I can't seem to get it? how to get a?
anonymous
  • anonymous
ZeHanz
  • ZeHanz
a²+144=400, so a²=?
anonymous
  • anonymous
16?
ZeHanz
  • ZeHanz
a²=256, so a=16, right!
anonymous
  • anonymous
thank you!
ZeHanz
  • ZeHanz
yw!

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