Question

the measure of two abjacent angles of parallelogram are in the ratio of 4:5 find the measure of each of the parallelogram ​

Answer 1

Answer:

Let ∠A and ∠B are two adjacent angles.

But we know that sum of adjacent angles of a parallelogram is 180°

∠A+∠B=180°

Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x

∠A+∠B=180°

4x+5x=180°

9x=180°

x=180/9

x=20°

∠A=4x=4×20=80°

∠B=5x=5×20=100°

Also ∠B+∠C=180°

[Since ∠B and ∠C are adjacent angles]

100°+∠C=180°

∠C=180°−100°

=80°

Now, ∠C+∠D=180°

[Since ∠C and∠D are adjacent angles]

80°+∠D=180°

∠D=180°−80°

=100°

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