If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:a.81∘b.54∘c.108∘d.72∘

In a parallelogram, adjacent angles are supplementary. This means that their sum is 180 degrees.

Let's denote the smaller angle as x. According to the problem, the larger angle is 2/3 times the smaller angle, so it can be represented as (2/3)x.

Since they are supplementary, we can set up the following equation:

x + (2/3)x = 180

Solving this equation will give us the value of the smaller angle, x.

First, combine like terms:

(1 + 2/3)x = 180

This simplifies to:

(5/3)x = 180

Next, to solve for x, divide both sides of the equation by 5/3, which is the same as multiplying by 3/5:

x = 180 * (3/5)

x = 108 degrees

So, the smallest angle of the parallelogram is 108 degrees, which corresponds to option c.