In the parallellogram ABCD, the sum of angle bisectors of two adjacent angles is _______.
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Step by Step Explanation:
- Following figure shows the parallelogram ABCD,
Let's assume, AO and DO are the angle bisectors of the adjacent angles ∠A and ∠D respectively.
Therefore, ∠DAO = ∠A/2,
∠ADO = ∠D/2.
- We know that the adjacent angles in a parallelogram are supplementary as they are formed by a straight line (e.g. AD) intersecting two paralle lines (e.g. AB and CD).
Therefore sum of the adjacent angles equals to 180°.
∠A + ∠D = 180° -----(1)
- Now, the sum of angle bisectors of the adjacent angles ∠A and ∠D = ∠DAO + ∠ADO
= ∠A/2 + ∠D/2
= (∠A + ∠D)/2
- Hence, the sum of angle bisectors of two adjacent angles is 90°.