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Asked by Perl Last Modified
Answer Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2. Let ∠A = 3x and ∠B = 2x
We know that the sum of the measures of adjacent angles is 180º for a parallelogram.
∠A + ∠B = 180º
3x + 2x = 180º
5x = 180º
∠A = ∠C = 3x = 108º (Opposite angles)
∠B = ∠D = 2x = 72º (Opposite angles)
Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º.
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sum of adjescent angles in a parallelogram=180°
since they are in the ratio 3:2
we can assume angle values like this. 3k and 2k
sum=3k+2k=5k
5k=180
k=180/5=36°
2k=2*36=72°
3k=3*36=108°
oposite angles are equal in parallelogram
hence angles of parallelogram are 72°,108°,72°,108°
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