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  • In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS. [Hint : Draw a line parallel to ST through point R.]

4. In Fig. 6.31, if PQ || ST, \angle PQR = 110° and \angle RST = 130°, find \angle QRS.
[Hint: Draw a line parallel to ST through point R.]

Answers (1)

best_answer

Draw a line AB parallel to the ST through R.
Since PQ || ST and ST || AB 
\Rightarrow AB || PQ

\anglePQR = \angleQRB = 110°   (Alternate interior angles)
\angleQRB = \angleQRS + \angleSRB .............(i)

Again, \angleRST + \angleSRB = 180°  (Interior angles of two parallels ST and RB)
=> \angleSRB = 180° - 130° =  50°  ( \angleRST = 130° )

Thus, \angleQRS = 110^0-50^0 = 60^0

Posted by

manish painkra

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