Measures of two adjacent angles of parallelogram are equal .Find the measures of all angles of the parallelogramare in the ratio 3:2 find the angles of parallelogram
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Let the angles be 3x , 2x , 3x , 2x
Sum of all the angles of parallelogram = 360
3x + 2x + 3x + 2x = 360
10x = 360
x = 36
3x = 3 * 36 = 108
2x = 2 * 36 = 72
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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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