Question

In the figure, line VP || line MS. Line DK is their transversal. If m∠DHP = 85° then


(1) m∠MGK = ......
(2) m∠VHD = ......
(3) m∠PHG = ......
(4) m∠HGS = .....

Answer 1

It is given that line VP ║ line MS, DK is the transversal and m$\angle DHP$ = 85°.

(1) $\angle DHP$ and $\angle MGK$ are alternate angles.
Because alternate angles are of the same measure, $\angle DHP$ = $\angle MGK$ = 85°.

(2) $\angle VHD$ and $\angle DHP$ form a linear pair.
∴ $\angle VHD$ + $\angle DHP$ = 180°
= $\angle VHD$ + 85° = 180°
= $\angle VHD$ = 180° – 85°
= $\angle VHD$ = 95°

(3) $\angle PHG$ and $\angle DHP$ form a linear pair.
∴ $\angle PHG$ + $\angle DHP$ = 180°
= $\angle PHG$ + 85° = 180°
= $\angle PHG$ = 180° – 85°
= $\angle PHG$ = 95°

(4) $\angle DHP$ and $\angle HGS$ are corresponding angles.
Because the measures of angles in each pair of corresponding angles formed by a transversal of the parallel lines are equal, $\angle DHP$ = $\angle HGS$ = 85°.