In the diagram, QP//ST:PQR = 34∘ ∘ QRS = 73∘ ∘ and RS = RT. Find SRT

Question 1 Report

In the diagram, QP//ST:PQR = 34 $^{\circ}$ QRS = 73 $^{\circ}$ and RS = RT. Find SRT

68

^{\circ}

102

^{\circ}

107

^{\circ}

141

^{\circ}

Answer Details

Construction joins R to P such that SRP = straight line

R = 180 $^{\circ}$ - 107 $^{\circ}$

< p = 180 $^{\circ}$ - (107 $^{\circ}$ - 34 $^{\circ}$ )

108 - 141 $^{\circ}$ = 39 $^{\circ}$

Angle < S = 39 $^{\circ}$ (corr. Ang.) But in $△$ SRT

< S = < T = 39 $^{\circ}$

SRT = 180 - (39 $^{\circ}$ + 39 $^{\circ}$ )

= 180 $^{\circ}$ - 78 $^{\circ}$

= 102 $^{\circ}$

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