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Find the measure of all four angles of a parallelogram whose consecutive angles are in the ratio 1 : 3

Find the measure of all four angles of a parallelogram whose consecutive angles are in the ratio 1 : 3

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
9 months ago
Dear Students

The ratio of two consecutive angles of a parallelogram = 1 : 3
Let x and 3x be the two consecutive angles.
We know that the sum of interior angles on the same side of the transversal is 180°.
Therefore, x + 3x = 180°
4x = 180°
x = 180°/4
x = 45°
⇒ 3x = 3(45°) = 135°
Thus, the measure of two consecutive angles is 45° and 135°.
As we know, the opposite angles of a parallelogram are equal.
Hence, the measure of all the four angles is 45°, 135°, 45°, and 135°.

Thanks

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