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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.]

                

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

\anglePQR = \angleQRF = 110^0  (Alternate interior angles)
\angleQRF = \angleQRS + \angleSRF .............(i)

Again, \angleRST + \angleSRF = 180^0 (Interior angles of two parallels ST and RF)
\Rightarrow \angle SRF =180^0-130^0 = 50^0  (\angleRST = 130^0, given)

Thus, \angleQRS = 110^0-50^0 = 60^0

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