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°
(4 Points)
35°
45°
55°
65°
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Since the two angles are vertical angles, they are equal to each other. We can set the expressions for the angles equal to each other:
\[
6x - 15 = 4x + 5
\]
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 we can find the measure of each angle by substituting \(x = 10\) back into either expression:
\[
6x - 15 = 6(10) - 15 = 60 - 15 = 45°
\]
\[
4x + 5 = 4(10) + 5 = 40 + 5 = 45°
\]
Thus, both angles measure \(45°\).
The measure of each angle is \( \text{45°} \).
\[
6x - 15 = 4x + 5
\]
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 we can find the measure of each angle by substituting \(x = 10\) back into either expression:
\[
6x - 15 = 6(10) - 15 = 60 - 15 = 45°
\]
\[
4x + 5 = 4(10) + 5 = 40 + 5 = 45°
\]
Thus, both angles measure \(45°\).
The measure of each angle is \( \text{45°} \).
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