Question

In the given figure , line RP || line MS and line DK is their transversal. $\angle$DHP = 85^°

Find the measures of following angles.

(i) $\angle$RHD (ii) $\angle$PHG

(iii) $\angle$HGS (iv) $\angle$MGK

Answer 1

(i) Since, RP is a straight line and ray HD stands on it, then
∠RHD + ∠DHP = 180^∘ (angles in a linear pair)
⇒∠RHD + 85^∘ = 180^∘
⇒∠RHD = 180^∘ − 85^∘ = 95^∘

(ii) Since the straight lines RP and DK intersect at H, then
∠PHG = ∠RHD (Vertically opposite angles)
⇒∠PHG = 95^∘

(iii) Since, the line RP || line MS and line DK is their transversal intersecting them at H and G, then
∠HGS = ∠DHP (Corresponding angles)
⇒∠HGS = 85^∘

(iv) Since, the straight lines MS and DK intersect at G, then
∠MGK = ∠HGS (Vertically opposite angles)
⇒∠MGK = 85^∘