+0

# Angle bisectors AX and BY of triangle ABC meet at a point I. Find angle C in degrees, if angle AIB is 109 degrees.

-1
95
5
+188

Angle bisectors AX and BY of triangle ABC meet at a point I. Find angle C  in degrees, if angle AIB is 109 degrees.

This is the (really bad) diagram. https://latex.artofproblemsolving.com/9/a/4/9a410e2228e9f2f01c8a6c8990c2ea3c9ebff2a0.png

Thank you so much!!!!!

Noori :)

Jun 9, 2020

#1
+976
+2

It's not a bad diagram. AoPS folks do a good job writing Asymptope code.

If you'll be so kind as to provide the week and problem number?

Thanks!

Jun 9, 2020
#2
+188
+2

I agree the diagram is great, but the lighting on the problem is bad :). Sure, Week 7 Problem 7

Jun 9, 2020
#3
+976
+2

So AIB is 109 degrees. IAB + IBA + 109 = 180, so IAB + IBA = 180 -109 = 71.

AX and BY are angle bisectors so IAB = CAB/2, and IBA = CBA/2. (CAB + CBA)/2 = 71.

Rearrange the last equation and you should be very close to your answer.

If you don't understand anything, feel free to ask!

hugomimihu  Jun 9, 2020
#4
+188
+2

Thank you so much!!!!!!!!! I got it. :)

Noori  Jun 9, 2020
#5
+976
+1

:)

Good job!

hugomimihu  Jun 9, 2020