The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

1. Break Down the Problem

We have two adjacent angles of a parallelogram that are in the ratio 3:2. Let's denote these angles as $3x$ and $2x$. Since the sum of adjacent angles in a parallelogram is $180^\circ$, we can set up an equation to find $x$.

2. Relevant Concepts

In a parallelogram, the following properties hold:

• Adjacent angles are supplementary: $\text{Angle}_1 + \text{Angle}_2 = 180^\circ$
• Given the ratio, we denote the angles as $3x$ and $2x$.

3. Analysis and Detail

Using the supplementary property: $3x + 2x = 180^\circ$ Combining like terms, we get: $5x = 180^\circ$ Now, solving for $x$: $x = \frac{180^\circ}{5} = 36^\circ$

Now we can find the measures of the angles:

• First angle: $3x = 3 \times 36^\circ = 108^\circ$
• Second angle: $2x = 2 \times 36^\circ = 72^\circ$

4. Verify and Summarize

To verify, we check if the sum of these two angles equals $180^\circ$: $108^\circ + 72^\circ = 180^\circ$ Thus, the calculations are confirmed.

Final Answer

The measures of the angles of the parallelogram are $108^\circ$ and $72^\circ$.