Question

The lengths of two adjacent sides of a parallelogram are in the ratio 4 : 5. Find the measure of all the angles of the parallelogram.

pls help me to solve this sum.
I want the answer step by step​

Answer 1

Answer:

Let the adjacent sides be =4x,5x‎ ‎

‎ ‎

According to the question.

4x+5x=180°

(sum of adjacent sides is 180°)

=9x= 180°

=x= $\frac{180}{9}$

=x= 20°

So, sides are -

$\rightarrow$4x=4×20= 80°

$\rightarrow$5x=5×20=100°

Answer 2

Answer:

Let ∠A and ∠B be adjacent angles

The 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  

Now lets take <C and <D as the opposite sides

~ As the opposite angles of a parallelogram are equal

<C = <A

So, <C equals to 80

<D = <B

So, <D equals to 100