Question

In figure , line RP || line MS and line DK is their transversal.∠ DHP = 85° Find the measures of following angles ∠ RHG and ∠ PHG​

Answer 1

Step-by-step explanation:

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)]Read more on Sarthaks.com - https://www.sarthaks.com/848944/the-given-figure-line-line-line-their-transversal-dhp-find-the-measures-following-angles