Question

The ratio of two adjacent anglss of a parallelogram is 2:3 find all the angles​

Answer 1

72°, 108°, 72°, and 108°

Explanation:

Theorem: Adjacent angles of a parallelogram are SUPPLEMENTARY

Supplementary means they add up to 180 degrees.

Thus, if one angle is "x", the other is "180 - x"

Since it is given two adjacent angles are in the ratio 2 is to 3, we can write:

`(x)/(180-x)=(2)/(3)`

We cross multiply and find x:

`(x)/(180-x)=(2)/(3)\\3x=2(180-x)\\3x=360-2x\\5x=360\\x=(360)/(5)\\x=72`

Thus, the other is:

180 - 72 = 108

The other angles (3rd and 4th) are same as these two. hence the 4 angles of the parallelogram are:

72°, 108°, 72°, and 108°