Question

A parallelogram has sides of length 36.4 centimeters and 21.5 centimeters. The lesser diagonal is 38.9 centimeters long. What are the interior angles of the parallelogram?

Answer 1

Interior angles are:`79.917995694105^@`and`79.917995694105^@`and
`100.082004305895^@` and `100.082004305895^@`

Explanation:

From the given data: A parallelogram has sides of length 36.4 centimeters and 21.5 centimeters. The lesser diagonal is 38.9 centimeters long. What are the interior angles of the parallelogram?

We have the half of the parallelogram forming a triangle with sides
`a=21.5` and `b=38.9" "`(shorter diagonal) and `c=36.4`

Interior angles are `B` and its opposite angle and `(180-B)` for the other two interior angles.

using cosine law

`B=cos^-1 ((a^2+c^2-b^2)/(2*ac))=cos^-1 ((21.5^2+36.4^2-38.9^2)/(2*(21.5)*(36.4)))`

`B=79.917995694105^@`
the other angle
`D=180-79.917995694105^@`

`D=100.082004305895^@`

God bless...I hope the explanation is useful.