Question

3. The measure of two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of each angle
of the parallelogram.
each of
nole​

Answer 1

Answer:

80°,100°

Step-by-step explanation:

Let 4x and 5x be the angles of the parellelogram which are adjacent

Hence,

4x+5x=180°(bcz opposite sides of a parellelogram are parallel)

Thus, 9x = 180°

. . . . . . x=20°

Putting value of x in 4x,5x

Hence, 4x=4(20)=80°

. . . . . . . 5x=5(20)=100

hope it helps you

Answer 2

Given :

• Two Adjacent sides of a parallelogram are in ratio of 4:5

To Find :

• Measure of each angle of parallelogram

Solution :

We are given that the adjacent sides of parallelogram are in ratio of 4:5.

Let, the angles be 4x and 5x

Also, we know that the opposite angles of parallelogram are equal. So, we can say that the measure of angles of parallelogram will be equal to 360° , by angle sum property of Quadrilateral.

So, the angles are, 4x, 5x, 4x and 5x

Now, by angle sum property of the quadrilateral

⇒4x + 5x + 4x + 5x = 360°

⇒9x + 9x = 360°

⇒18x = 360°

⇒x = 360/18

⇒x = 20

$\therefore$ Value of x is 20°

____________________________

Now, we can find measure of all the angles of parallelogram :

• 4x = 4(20) = 80°

• 5x = 5(20) = 100°

So, all the four angles are : 80°,80°,100° and 100°