The measure of two adjacent angles of a parallelogram are in the ratio 3:2 .The measure of smallest of the angles of the parallelogram in degree is ____ degree.

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Detailed Solution

Concept- The measure of smallest of the angles of the parallelogram in degree is 72 degree.
First, we need be aware of the parallelogram's property, which states that the sum of all its angles is

, and the sum of its adjacent angles is

. We must thus suppose that any angle is 3 x and that any angle next to it is 2 x. The value of

can then be determined by adding and equating it with 180, i.e.

. After finding the value of

, we will put that in 3 x and 2 x and then compare which value of angle is smaller.
We know that the sum of the two adjacent angles of a parallelogram is

The given ratio of the angles is 3: 2
Let the angles be

and

to keep up with the given ratio.

and

Largest angle

and Smallest angle

.
Hence, the answer is