Question

In the given figure, line RP || line MS and line DK is their transversal. ∠DHP = 85°.

Find the measures of the following angles.

1. ∠RHD
2. ∠PHG
3. ∠HGS  
4. ∠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^∘ 

⇒ ∠RHD = 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^∘