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.
Question
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.
Solution
In a parallelogram, adjacent angles are supplementary. This means that they add up to 180 degrees.
Given that the ratio of the two angles is 3:2, we can set up the equation 3x + 2x = 180, where x is a common multiplier.
Solving for x gives us x = 180 / 5 = 36 degrees.
Therefore, the measures of the two angles are 3 * 36 = 108 degrees and 2 * 36 = 72 degrees.
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