Question

in the figure m angle a:८५ and m angle d : ११० find m angle b and m angle c
​

Answer 1

Answer:

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



Find the measures of following angles.

(i) ∠∠RHD  (ii) ∠∠PHG

(iii) ∠∠HGS  (iv) ∠∠MGK

 

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∘