Foreverisabell 2 years ago Find the measure of angle DCA if D is the incenter of the triangle ABC. Explain step by step please!

1. Foreverisabell

2. Foreverisabell

@ZeHanz this one.

3. ZeHanz

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

4. Foreverisabell

Also in this one, would y = 60?

5. Foreverisabell

Alright,

6. ZeHanz

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

7. Foreverisabell

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

8. ZeHanz

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

9. Foreverisabell

111 is the measure of ABC

10. Foreverisabell

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

11. Foreverisabell

which is c?

12. 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.

13. Foreverisabell

yeah I got 42.

14. ZeHanz

That's right!

15. Foreverisabell

But why did you times 2 times each?

16. Foreverisabell

never mind I know why now.

17. Foreverisabell

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

18. 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...

19. ZeHanz

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

20. Foreverisabell

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

21. Foreverisabell

Measure of DCA = 21 degrees it seems really small?

22. ZeHanz

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

23. Foreverisabell

alright

24. Foreverisabell

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

25. Foreverisabell

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?

26. Foreverisabell

@ZeHanz

27. ZeHanz

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

28. Foreverisabell

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

29. Foreverisabell

@ZeHanz

30. ZeHanz

a²+144=400, so a²=?

31. Foreverisabell

16?

32. ZeHanz

a²=256, so a=16, right!

33. Foreverisabell

thank you!

34. ZeHanz

yw!