How to find the value of x and y in a parallelogram

5x - 20 = 2x +43 -> 5x-2x= 43+20 -> 3x=63 -> x=21 therefore x=21 

(2x+43) + (4y-5x)=180  -> 2x+43+4y-5x=180 (because adjacent angles in a parallelogram equals 180) 

4y-3x=180-43 -> 4y= (100-43)+3x -> 4y = (180-43)+3(21) (because x=21) 

therefore 4y=137+63 -> 4y=200 -> therefore y=200/4 therefore y=50 

therefore y=50 and x=21

Answer:

23. x = 11, y = 14

24. x = 10.5°

25. x = 23°, y = 50°

26. x = 3, y = 5

Step-by-step explanation:

Properties Used:

• The diagonals of a parallelogram bisect each other
• Consecutive angles of a parallelogram are supplementary

23.

Solving for x,

x + 14 = 25

⇒ x = 25 - 14

⇒ x = 11

Solving for y,

y + 16 = 30

⇒ y = 30 - 16

⇒ y = 14

24.

(11x - 18.5) + (8x - 1) = 180

⇒ 19x - 19.5 = 180

⇒ 19x = 180 + 19.5

⇒ 19x = 199.5

⇒ x = 199.5/19

⇒ x = 10.5°

25.

Solving for x,

(4x + 13) + (3x + 6) = 180

⇒ 7x + 19 = 180

⇒ 7x = 180 - 19

⇒ 7x = 161

⇒ x = 161/7

⇒ x = 23°

Solving for y,

(y + 45) + (4y - 15) = 180

⇒ 5y + 30 = 180

⇒ 5y = 180 - 30

⇒ 5y = 150

⇒ y = 150/5

⇒ y = 50°

26.

Solving for x,

2x + 11 = 5x + 2

⇒ 11 - 2 = 5x - 2x

⇒ 9 = 3x

⇒ x = 9/3

⇒ x = 3

Solving for y,

4y - 3 = 3y + 2

⇒ 4y - 3y = 2 + 3

⇒ y = 5

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Solution:

Given, the figure represents a parallelogram.

We have to find the values of x and y.

We know that the adjacent angles of a parallelogram are supplementary.

So, 120° + (5x + 10)° = 180°

130° + 5x = 180°

5x = 180° - 130°

5x = 50°

x = 50°/5

x = 10°

We know that the opposite angles of a parallelogram are equal.

6y = 120°

y = 120°/6

y = 20°

Therefore, the values of x and y are 10° and 20°.

✦ Try This: Find the values of x and y in the following parallelogram.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 161

Find the values of x and y in the following parallelogram.

Summary:

The values of x and y in the given parallelogram are 10° and 20°.

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