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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.


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Solution

The measure of each of the angles of the parallelogram

Let the measures of two adjacent angles are 3x and 2x.

As the sum of two adjacent angles of a parallelogram is 180°.

Then,

3x+2x=180°thatareintheratio3:25x=180°x=36°

Now,

3x=3×36°=108°2x=2×36°=72°

The opposite angles of a parallelogram are equal. So, a measure of each of the angles of a parallelogram is

108°,72°,108°,72°.

Hence, the measure of each of the angles of a parallelogram is

108°,72°,108°,72°.


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