Question

what is the measure of two adjacent parallelogram in the ratio 4:5?​

Answer 1

Step-by-step explanation:

Let ∠A and ∠B are two adjacent angles.

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

∠A+∠B=180o

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

 ∠A+∠B=180o

4x+5x=180o

9x=180o

x=180/9

x=20o

∠A=4x=4×20=80o

∠B=5x=5×20=100o

Also ∠B+∠C=180o [Since ∠B and 

∠C are adjacent angles]

100o+∠C=180o

∠C=180o−100o=80oNow, ∠C+∠D=180o  [Since ∠C and 

∠D are adjacent angles]

80o+∠D=180o

∠D=180o−80o=100o

Answer 2

Answer:

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.