Question

Quadrilateral PQRS is a parallelogram. Find the value of x when angle P = (23x + 5) and and angle Q = (13x - 5)

Answer 1

To find the value of x for angles P and Q in a parallelogram, you can set the two angle expressions equal to each other and solve for x. The solution in this case yields x = -1.

Step-by-step explanation:

The student is asking about the properties of angles in a parallelogram. In a parallelogram, opposite angles are equal. Since PQRS is a parallelogram, we know that ∠P is equal to ∠Q. Therefore, we can set up the following equation based on the information given:

(23x + 5) = (13x - 5)

Now, we solve for x:

1. Add 5 to both sides of the equation: 23x + 10 = 13x
2. Subtract 13x from both sides: 10x + 10 = 0
3. Subtract 10 from both sides: 10x = -10
4. Divide both sides by 10: x = -1

Therefore, the value of x is -1.