Question

In a parallelogram PQRS, angle P= (3x-20)° , angle Q =(y-15)° , and angle R = (x+40)° , then find the values of x and y

Answer 1

angle p=angle r
3x-20=x+40
3x+x=40+20
4x=60
x=60/4
x=15
angle p=3×15-20=25
angle p+ angle q=180(co interior angle)
25+ y-15=180
y-15=180-25
y=155+15
y=170

Answer 2

The values of x and y are 30° and 125°, respectively.

Step-by-step explanation:

Given: A parallelogram PQRS, ∠P = (3x-20)°, ∠Q = (y-15)°, and ∠R = (x+40)°

To Find: The values of x and y

Solution:

• Finding the values of x and y in a parallelogram PQRS

In the parallelogram PQRS, ∠P = ∠R,

⇒ 3x - 20 = x + 40

⇒ 3x - x = 20 + 40

⇒ 2x = 60

⇒ x = 30°

And, ∠Q + ∠R = 180°,

⇒ y - 15 + x + 40 = 180

⇒ y + x = 180 - 25 = 155°

putting x = 30°, we get

⇒ y + 30 = 155°

⇒ y = 155 - 30 = 125°

⇒ y = 125°

Hence, the values of x and y are 30° and 125°, respectively.