Question

give fast answer
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Answer 1

Given:-

• RP||MS & DK is the Transversal.
• DK bisects RP & MS at H and G respectively.
• ∠DHP = 85°.

To Find:-

• ∠RHD
• ∠PHG
• ∠HGS
• ∠MGK

Solution:-

∠RHD+∠DHP = 180° [Linear Paired Angles]

∠RHD+85° = 180°

∠RHD = 180°-85°

∠RHD = 95°

• $\longmapsto\;\Large\sf{∠RHD = 95°}$

∠RHD = ∠PHG [Vertically Opposite Angles]

95° = ∠PHG

• $\longmapsto\;\Large\sf{∠PHG = 95°}$

∠PHG+∠HGS = 180° [Co-interor Angles]

∠HGS+95° = 180°

∠HGS = 180°-95°

∠HGS = 85°

______✯_____

∠HGS = ∠DHP [Corresponding Angles]

∠HGS = 85°

• $\longmapsto\;\Large\sf{∠HGS = 85°}$

∠HGS = ∠MGK [Vertically Opposite Angles]

85° = ∠MGK

• $\longmapsto\;\Large\sf{∠MGK = 85°}$

☞ Linear Pair Angles are Supplementary.

☞ Co-interor Angles are Supplementary.

☞ Vertically Opposite Angles are Equal.

☞ Corresponding Angles are Equal.

$\bold{@MrMonarque}$

Hope It Helps You ✌️