Question

Find the value of x and y for which [] CARE is a parallelogram.

Answer 1

Step-by-step explanation:

Answer

Adjacent angles of a parallelogram are supplementary.

⇒120

∘

+(5x+10)

∘

=180

∘

⇒5x+10

∘

+120

∘

=180

∘

⇒5x=180

∘

−130

∘

⇒5x=50

∘

⇒x=10

∘

Also, opposite angles of parallelogram are equal.

⇒6y=120

∘

⇒y=20

∘

Answer 2

The value of x and y must be 10° and 20° respectively such that CARE is a parallelogram.

Given:

A parallelogram is given. # angles are given as 6y , 120 ° and (5x+10) .

To find:

The values of x and y.

Solution:

We know that the opposite sides of a parallelogram are parallel.

Therefore from the figure we can see that the angles marked 1 are co-interior angles as they fall on the same side of the parallel sides.

We know that co-interior angles are supplementary.

Therefore :

$120 + (5x+10) = 180\\or, 130 + 5x = 180\\or,5x = 180-130\\or, 5x = 50 \\or, x = 50/5\\or, x = 10$

Therefore the value of x is 10.

Now again the angles marked y and 5x + 10 are co-interior.

So using the same property as above we can write the simple equation as:

$y + 5x + 10 = 180$

$or, 6y + 5(10) + 10 = 180\\or, 6y + 60 = 180\\or, 6y = 180-60\\or, y =20$

Therefore the value of y is 20° .

To learn more about parallelogram visit:

https://brainly.in/question/47203834

https://brainly.in/question/9383525

#SPJ3