n
Solve the following:
In the adjoining figure, if
La + 2b = 180 ° the prove
that line [ // line m.
Answers
Answer:
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Page No 17:
Question 1:

In the given figure , line RP || line MS and line DK is their transversal. ∠∠DHP = 85°
Step-by-step explanation:
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∘
