Angle bisectors TX and UY of triangle TUV meet at point I. Find all possible values of angle V if angle TIU = 109 degrees. As your answer, enter the number of degrees in angle V. If you find more than one possibility, list the possible values in increasing order, separated by commas.
+129839 Let < YTU = x
Let < XUT = y
Let < TVU = z
< YIT = <XIU = 71
And we have the following system
(1/2) x + (1/2)y + 109 = 180 → x + y = 142
x + y + z = 180
(1/2)x + 71 + (1/2)y + 71 + 109 + z = 360 → x + y + 2z = 218
So....
x + y = 142 (1)
x + y + z = 180 (2)
x + y + 2z = 218 (3)
Subtract (1) from (2) and z = 38° = < TVU = "angle V "
And..... y = 142 – x → (1/2)y = 71 - (1/2)x
As Melody always says, "This is what I think. "
