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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