Question

In figure 3 line AB || line CD and line PQ is transversal. measures of one of the angle given. find measure of the following ​

Answer 1

(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

∘

)