find each angle of a parallelogram if two consecutive angles are in the ratio 1 : 3

Any two consecutive angles are in the ratio 1: 3, then opposite angles will be the same. 
Let the one angle be x then 2(1x) + 2(3x) = 360 (ANGLE SUM PROPERTY)
2x + 6x = 360
8x = 360 
x = 360/8
x = 45
1x = 45
3x = 3 x 45 = 135
2 x 45 + 2 x 135 = 90 + 270 = 360

 
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