Question

complete the following activity.
1) In the figure Line ABll line CD and line PQ is their tranvesversal. which intersects line AB and line CD intersects at points R. and S rpespectively .


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Answer 1

Step-by-step explanation:

(i) Since AB is a straight line and ray RT stands on it, then

∠ART+∠BRT=180 ∘ (Angles in a linear pair)

⇒∠ART+105∘=180∘

⇒∠ART=180 ∘−105∘=75 ∘

(ii) Since line AB ∥ line CD and line PQ is a transversal intersecting them at R and T, then

∠ART=∠CTQ(corresponding angles)

⇒75∘ =∠CTQ

⇒∠CTQ=75∘

(iii) Since line AB ∥ line CD and line PQ is a transversal intersecting them at R and T, then

∠BRT=∠DTQ(corresponding angles)

⇒105∘=∠DTQ

⇒DTQ=105∘

(iv) Since line AB and line PQ intersect at point R, then

∠PRB=∠ART (vertically opposite angles)

⇒∠PRB=75∘ (∵∠ART=75∘)