TQ is tangent to circle XYTR, < YXT = 32o, RTQ = 40o. find < YTR

Explanation

< TXR = < QTR = 40o (alternate segment)

< TWR = < TXR = 40o(Angles in the same segments)
< YXR = 40o + 32o = 72o

< YXR + < YTR = 180o(Supplementary)

72o + < YTR = 180o

< YTR = 180o - 72o

= 108o