1.

The bisector of two adjacent angles of a parallelogram intersect at which angle ?☘Don't spam☘‼Need answer with explanation ‼✔✔​

Answer»

Let the ABCD be parallelogram

GIVEN:-

  • ∠EAB = ½∠A

  • ∠EBA = ½∠B

To FIND:-

  • Measure of ∠AEB

Solution:-

➥ As we know, Sum of adjacent angles of a parallelogram is 180°.

Hence,

∠ A + ∠B = 180°

➟ ½∠A + ½∠B = ½ of 180°

➟ ½∠A + ½∠B = 90°

➟ ∠EAB + ∠EBA = 90° ------- eq. 1

➥ As we know, Sum of all angles of a TRIANGLE is 180°

Hence,

Sum of angles of ∆ EAB = 180°

➟ ∠EAB + ∠EBA + ∠AEB = 180°

➟ ( ∠EAB + ∠EBA ) + ∠AEB = 180°

➟ 90° + ∠AEB = 180° [ By equation 1 ]

➟ ∠AEB = 180° - 90°

∴ ∠AEB = 90°

Answer:-

The bisector of two adjacent angles of a parallelogram intersect at right angle ( 90° ).

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