Question

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

35°

45°

55°

65°

Answer 1

To find the measure of each angle given that they are vertical angles, we can set them equal to each other because vertical angles are congruent.

We have:

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

Now, let's solve for \(x\).

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

2. Add 15 to both sides:
\[
2x = 20
\]

3. Divide by 2:
\[
x = 10
\]

Now that we have the value of \(x\), we can find the measure of each angle.

1. Calculate the first angle:
\[
6x - 15 = 6(10) - 15 = 60 - 15 = 45°
\]

2. Calculate the second angle:
\[
4x + 5 = 4(10) + 5 = 40 + 5 = 45°
\]

Therefore, both vertical angles measure **45°**.

So the answer is **45°**.