The measure of two adjacent angles of a parallelogram are in the ratio 4:5 .Find the measure of each of the angles of the parallel

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1. Step-by-step explanation:

   Given :–

   The measure of two adjacent angles of a parallelogram are in the ratio 4:5 .

   To find:–

   Find the measure of each of the angles of the parallelogram?

   Solution:–

   Given that

   The ratio of the measure of two adjacent angles of a parallelogram = 4:5

   Let they be 4X° and 5X°

   We know that

   The sum of adjacent angles in a Parallelogram are supplementary.

   => 4X° + 5X° = 180°

   => 9X° = 180°

   => X° = 180°/9

   =>X° = 20°

   Now ,

   4X° = 4(20°)=80°

   5X°=5(20°)=100°

   We know that

   Opposite angles are equal in a Parallelogram

   The opposite angle of 80° = 80°

   The opposite angle of 100° = 100°

   Answer:–

   The all angles in the given Parallelogram are

   80°,100° ,80° and 100°

   Used formulae:–

   In a Parallelogram,

   • The sum of adjacent angles are supplementary.
   • The opposite angles are equal.

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