Question

WILL GIVE 20 POINTS! PLEASE PLEASE ANSWER THIS!!!

Given: KLMN is a parallelogram,

KA

− angle bisector of ∠K

LA

− angle bisector of ∠L

Prove: m∠KAL = 90°

answer in format LKM+?= (something degrees) by reason ?

Answer 1

∠ KAL = 90° (Proved)

Explanation:

See the attached diagram.

As KLMN is a parallelogram, so ∠K + ∠ L = 180°

⇒
`(1)/(2)\angle K + (1)/(2)\angle L = 90^(\circ)` ............ (1)

Now, given that,
`\angle AKL = (1)/(2) \angle K` and
`\angle ALK = (1)/(2) \angle L`

So, ∠ AKL + ∠ ALK = 90° {From equation (1)}

Now, from Δ KAL, ∠ AKL + ∠ ALK + ∠ KAL = 180°

⇒ 90° + ∠ KAL = 180°

⇒ ∠ KAL = 90° (Proved)