Question

line l is parallel to line m
i) ∠RPA = ∠PQC   (_________________________)  ii) m∠APQ + m∠CQP = 180°  (__________________________)

 Interior angles theorem, Linear pair axiom

Corresponding angles theorem, Interior angles theorem

Corresponding angles test, Interior angles theorem Interior angles test,

Corresponding angles test​

Answer 1

$\bigstar \: \boxed{\sf{\color{Pink}{Answer:}}}$

(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∘

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Answer 2

Answer:

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