Question

If angle 1 and angle 2 are vertical angles, if Angle 1=(8x-3) and Z2=(x+32) find x.

Answer 1

To find the value of x when angle 1 and angle 2 are vertical angles with expressions (8x - 3) and (x + 32), set the expressions equal to each other, solve for x, and you get x = 5.

Step-by-step explanation:

If angle 1 and angle 2 are vertical angles, then they are congruent, which means they have equal measures. The algebraic expressions for Angle 1 and Angle 2 are given as Angle 1 = (8x - 3) and Angle 2 = (x + 32). To find the value of x, set these two expressions equal to each other because vertical angles have the same measure.

Therefore, we have:
(8x - 3) = (x + 32).

To solve for x, follow these steps:

1. Subtract x from both sides: 8x - x - 3 = x - x + 32, which simplifies to 7x - 3 = 32.
2. Add 3 to both sides: 7x - 3 + 3 = 32 + 3, which simplifies to 7x = 35.
3. Divide both sides by 7: 7x / 7 = 35 / 7, which simplifies to x = 5.

So the value of x is 5