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Lines and Angles
Question
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In figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint. Draw a line parallel to ST through point R.]

Answer

Construction: Draw a line RU parallel to ST through point R.

∠RST +  ∠SRU = 180°
| Sum of the consecutive interior angles on the same side of the transversal is 180°
⇒ 130° + ∠SRU = 180°
⇒    ∠SRU = 180° - 130° = 50°    ...(1)
∠QRU = ∠PQR = 110°
| Alternate Interior Angles
⇒ ∠QRS + ∠SRU = 110°
⇒ ∠QRS + 50° = 110° | Using (1)
⇒    ∠QRS = 110° - 50° = 60°.

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