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

Question 1 Report

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

108

^{\circ}

121

^{\circ}

140

^{\circ}

148

^{\circ}

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 $^{\circ}$

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