Short Answer TypeIn figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint. Draw a line parallel to ST through point R.]
In figure, EF is a transversal to two parallel lines AB and CD, GM and HL are the bisectors of the corresponding angles EGB and EHD. Prove that GM || HL.
[Hint. First prove that ∠EGM = ∠GHL]
AB || CD and a transversal EF intersects them
∴ ∠EGB = ∠GHD
| Corresponding Angles
⇒ 2 ∠EGM = 2 ∠GHL
| ∵ GM and HL are the bisectors of ∠EGB and ∠EHD respectively.
⇒ ∠EGM = ∠GHL
But these angles form a pair of equal corresponding angles for lines GM and HL and transversal EF.
∴ GM || HL.
In figure, PQ || RS and T is any point as shown in the figure then show that
∠PQT + ∠QTS + ∠RST = 360°.
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