In figure 2.5, 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

Given: RP ∥ line MS and line DK is their transversal.

(i) ∠ DHP + ∠ RHD = 180° (linear pair angle) means that linear pair is a pair of adjacent, supplementary angle. Adjacent means next to each other, and supplementary means that measures of the two angles add up to equal 180 °.

∠ DHP + ∠ RHD = 180°

85° + ∠ RHD = 180° (∠ DHP = 85° given)

∠ RHD = 180° -85°

∠ RHD = 95°

(ii) ∠ RHD ≅ ∠ PHG (vertically opposite angles formed are congruent)

So, ∠ PHG = 95°

(iii) line RP || line MS (given)

∠ DHP ≅ ∠ HGS (corresponding angles) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent.

∠ DHP = 85° (given)

So, ∠ HGS = 85°

(iv) ∠ HGS ≅ ∠ MKG (vertically opposite angles formed are congruent)

So, ∠ MKG = 85°