The bisectors of any two adjacent angles of a parallelogram intersect at: (a)`30^@` (b) `45^@` (c) `60^@` (d) `90^@`

Explanation

Given: Let ABCD is a parallelogram, OA and OD are the bisectors of adjacent angles `angleA and angleD`

Solution: Now, ABCD is a parallelogram

`therefore` AB||DC (Opposite sides of the parallelogram are parallel)

AB || DC and AD is the transversal, Therefore, `angleBAD + angleCDA = 180^@`(Sum of interior angles on the same side of the transversal is `180^@`)

`angle1 + angle2 = 90^@` (AO and DO are angle bisectors) ____1

In `triangleAOD`

`angle1 + angleAOD + angle2 = 180^@`

`angleAOD + 90^@ = 180^@` [From 1]

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