Question

Find the value of x if P Q R S spaceis a parallelogram.

Answer 1

Answer:

The value of x is 15.

Step-by-step explanation:

Given

PQRS is a parallelogram.

∠Q = (3x + 25)°

∠S = (5x - 5)°

To determine

The value of x = ?

We know that both pairs of opposite angles of a parallelogram are congruent.

As ∠Q and ∠S are opposite angles of a parallelogram. Therefore,  ∠Q and ∠S are equal.

Thus,

∠Q = ∠S

substitute ∠Q = (3x + 25)° and ∠S = (5x - 5)° in the equation

(3x + 25)°  = (5x - 5)°

subtract 25 from both sides

3x + 25 - 25 = 5x - 5 - 25

3x = 5x - 30

flip the equation

5x - 30 = 3x

add 30 to both sides

5x - 30 + 30 = 3x + 30

5x = 3x + 30

subtract 3x from both sides

5x - 3x = 3x + 30 - 3x

2x = 30

divide both sides by 2

2x/2 = 30/2

x = 15

Therefore, the value of x is 15.