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प्रश्न
In the given figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint: Draw a line parallel to ST through point R.]
आकृति
योग
उत्तर
Construction: XY || ST is drawn through point R.
PQ || ST ...(1) Given
XY || ST ...(2) By construction
From equations (1) and (2),
PQ || XY ...(3)
XY || ST By construction
∠RST + ∠SRY = 180° ...(Sum of interior angles on the same side)
⇒ 130° + ∠SRY = 180°
⇒ ∠SRY = 180° − 130°
⇒ ∠SRY = 50°
PQ || XY ...(3)
∴ ∠PQR = ∠QRY ...(Alternate angles)
110° = ∠QRS + ∠SRY
110° = ∠QRS + 50°
∠QRS = 110° − 50°
Thus, ∠QRS = 60°
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