Question

ZA and ZB are vertical angles. If m ∠ A = (2x + 1) and

m ∠ B = (x + 10), then find the value of x.

Answer 1

To find the value of x when ZA and ZB are vertical angles with m ∠ A = (2x + 1) and m ∠ B = (x + 10), we set the expressions equal and solve for x to find that x = 9.

Step-by-step explanation:

Given that ZA and ZB are vertical angles, and the measure of angle A (m ∠ A) is given by (2x + 1) and the measure of angle B (m ∠ B) is given by (x + 10), we can determine the value of x using the property that vertical angles are congruent.

Setting the measurements equal to each other gives us the equation 2x + 1 = x + 10. To solve for x, we follow these steps:

1. Subtract x from both sides: 2x + 1 - x = x + 10 - x, which simplifies to x + 1 = 10.
2. Subtract 1 from both sides: x + 1 - 1 = 10 - 1, which gives us x = 9.

The value of x is therefore 9.