Question

If the PQRS is a parallelogram find the values X and Y.
Q (4y+7)
R (10y- 37)

Answer 1

Answer:

sum of the adjacent angles of parallelogram is supplementary.

Therefore,

Q + R = 180°

4y+7 + 10y-37 = 180°

14y - 30° = 180°

14y = 210°

y = 210°/14

y = 15°

Could not found X in the question.

Answer 2

Value of x is 4 and  value of Y is 15  if PQRS is a parallelogram and ∠Q = (4y + 7)° , ∠R = (10y - 37)° . Sides QR  = 19x - 9 and PS =  13x + 15

Given:

• PQRS is a parallelogram
• ∠Q = (4y + 7)°
• ∠R = (10y - 37)°
• QR  = 19x - 9
• PS =  13x + 15

To Find:

• values X and Y

Solution:

• Opposite sides of parallogram are equal and parallel
• Adjacent angles of parallelogram are supplementary
• Opposite angles of parallelogram are equal

Step 1:

As ∠Q and ∠R are adjacent angles hence they adds up to 180°

4y + 7  + 10y - 37  = 180

=> 14y - 30 = 180

=> 14y = 210

=> y = 15

Hence  value of Y is 15

Step 2:

QR and PS are opposite sides hence equal in length

19x - 9 = 13x + 15

=> 6x = 24

=> x = 4

Value of x is 4

(Although Question misses some information but same has been added by adding missing figure)