4. The measures of two adjacent angles of a parallelogram are in the ratio of 4:5. Find the measure of each angle of the parallelogram.
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A parallelogram, being a quadrilateral has four interior angles. The neighbouring angles here are consecutive angles. A diagonal splits a vertex angle into the two; those are the adjacent angles.
Two consecutive angles are supplements; one acute, the other obtuse.
By data, they are in the ratio of 4:5 = 4x:5x.
So, 4x+5x = 180°
9x = 180°
x = 20°
4x = 80° and 5x = 100°
Hence, the consecutive angles in the parallelogram are 80° and 100°.
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