Question

Find the measure of the angle that is alternate to 23 in a set of parallel lines.​

Answer 1

Answer:

ANSWER:

(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∘