Question

In the figure, line AB ll line CD and line XY is their transversal. If ∠PQC = 75⁰, then find the measure of ∠XPB.​

Answer 1

Answer:

(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  

∘

)

Answer 2

Answer:

line AB ll line CD and line XY is their transversal. If ∠PQC = 75⁰, then find the measure of ∠XPB.