Question

in the figure below ,PQ and RS are parallel. calculate all other angles in the figure​

Answer 1

Answer:

Given, Rs || PQ AND RQ is a transversal

so angle SRQ = < RQP = 40° (alternate interior angle)

now RS || PQ and SP is a transversal

so angle RSP = angle SPQ = 60° (Alternate interior angle)

in ∆TRS,

angle RST + SRT + RTS = 180° ( ANGLE SUM PROPERTY)

SO angle RTS = 180° - (60° + 40°) = 80°

NOW angle RTS = angle PTQ = 80°(vertically opposite angles)

ALSO angle STQ + PTQ = 180° ( Linear Pair)

so angle STQ = 180 - 80° = 100°

Now angle RTP = angle STQ = 100°

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