1.

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. ∠DHP = 85° …..(i) 

∠DHP + ∠RHD = 180° [Angles in a linear pair] 

85° + ∠RHD = 180° 

∴ ∠RHD = 180°- 85° 

∴ ∠RHD = 95° …..(ii) 

ii. ∠PHG = ∠RHD [Vertically opposite angles] 

∴ ∠PHG = 95° [From (ii)]

iii. line RP || line MS and line DK is their transversal. [Corresponding angles] 

∴ ∠HGS = ∠DHP …..(iii) [From (i)] 

iv. ∠HGS = 85° [Vertically opposite angles] 

∴ ∠MGK = ∠HGS ∠MGK = 85° [From (iii)]



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