TQ is tangent to circle XYTR, < YXT = 32∘ ∘ , RTQ = 40∘ ∘ . Find < YTR

TQ is tangent to circle XYTR, < YXT = 32${}^{\circ }$, RTQ = 40${}^{\circ }$. Find < YTR

Answer Details

< TWR = < QTR = 40${}^{\circ }$ (alternate segment)

< TWR = < TXR = 40${}^{\circ }$(Angles in the same segments)

< YXR = 40${}^{\circ }$ + 32${}^{\circ }$ = 72${}^{\circ }$

< YXR + < YTR = 180${}^{\circ }$(Supplementary)

72${}^{\circ }$ + < YTR = 180${}^{\circ }$

< YTR = 180${}^{\circ }$ - 72${}^{\circ }$

= 108${}^{\circ }$