Question

Two vertical angles are given as (6x−15)° and (4x+5)°. What is the measure of each angle?

Answer 1

Vertical angles are equal, which means we can set the two expressions for the angles equal to each other:

\[
6x - 15 = 4x + 5
\]

To solve for \(x\), we can first get all the \(x\) terms on one side and the constant terms on the other:

1. Subtract \(4x\) from both sides:
\[
6x - 4x - 15 = 5
\]
\[
2x - 15 = 5
\]

2. Next, add 15 to both sides:
\[
2x = 5 + 15
\]
\[
2x = 20
\]

3. Now, divide both sides by 2:
\[
x = 10
\]

Now that we have the value of \(x\), we can find the measure of each angle by substituting \(x\) back into either of the angle expressions.

Let's substitute \(x = 10\) into the first angle:
\[
6x - 15 = 6(10) - 15 = 60 - 15 = 45°
\]

Now, let's check \(x = 10\) in the second angle:
\[
4x + 5 = 4(10) + 5 = 40 + 5 = 45°
\]

Both angles are indeed \(45°\).

Thus, the measure of each angle is:
\[
\boxed{45°}
\]