Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, en

Question

3 years ago

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Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, en

ter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.

Mathematics

1 answer:

emmasim [6.3K] · Answer 1 · 2022-04-29T21:41:35+03:00

emmasim [6.3K]3 years ago

4 0

Check the picture attached.

let m(VTI)= m(ITU)=a and let m(VUI)= m(IUT)=b

Then, in triangle TUV:

2a+2b+c=180°

2(a+b)+c=180°

c=180°-2(a+b)

In triangle TUI:

a+b+109°=180°

a+b=180°-109°=71°

substitute in c=180°-2(a+b):

c=180°-2(a+b)=180°-2*71°=180°-142°=38°