Question

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Answer 1

Step-by-step explanation:

given the ratio between the two adjacent angles of a parallelogram is 4 : 5

let the two adjacent angles of the paralelegram be 4x and 5x respectively.

we know that,

» sum of two adjacent angles in a parallelogram = 180°

➡ 4x + 5x = 180°

➡ 9x = 180°

➡ x = 180/9

➡ x = 20°

therefore the two adjacent angles are :-

4x = 4 × 20 = 80°

5x = 5 × 20 = 100°

now, also the opposite angles of a parallelogram is same. it's one of it's properties. opposite angles are same in a parallelogram.

hence, all the angles of the parallelogram are 80°, 100°, 80° and 100°

Answer 2

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°