Question

In trapezium HARE, EP and RP are bisectors of ∠E and ∠R respectively. Find ∠HAR and ∠EHA.

Answer 1

As EP and PR are angle bisectors of ∠REH and ∠ARE respectively.   ...[Given]

Since, HARE is a trapezium,

Therefore, ∠E + ∠H = 180° and ∠R + ∠A = 180°

⇒ ∠PER + ∠PEH + ∠H = 180° and ∠ERP + ∠PRA + ∠RAH = 180°

⇒ 25° + 25° + ∠H = 180° and 30° + 30° + ∠A = 180°

⇒ 50° + ∠H = 180° and 60° + ∠A = 180°

⇒ ∠H = 130° and ∠A = 120°, i.e. ∠EHA = 130° and ∠HAR = 120°