In the parallellogram ABCD, the sum of angle bisectors of two adjacent angles is _______.


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Answer:

90°

Step by Step Explanation:
  1. 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.
  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)
  3. Now, the sum of angle bisectors of the adjacent angles ∠A and ∠D = ∠DAO + ∠ADO
    = ∠A/2 + ∠D/2
    = (∠A + ∠D)/2
    = 180/2
    = 90°
  4. Hence, the sum of angle bisectors of two adjacent angles is 90°.

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