Question
∠KLM and ∠MLP are supplementary angles. The angles have the following measures: m∠KLM=(x+30)°and m∠MLP=(2x+60)°. What is an equation to solve for the unknown angle measures? Write the equation in simplest terms.(1 point)
___x°+___=180
___x°+___=180
Answers
GPT-4o mini
Since ∠KLM and ∠MLP are supplementary angles, their measures add up to 180 degrees. We can express this relationship mathematically using the measures given.
The measures of the angles are:
- m∠KLM = (x + 30)°
- m∠MLP = (2x + 60)°
Setting up the equation we have:
\[
(x + 30) + (2x + 60) = 180
\]
Now we can simplify this:
1. Combine like terms: \(x + 2x + 30 + 60 = 180\)
2. This simplifies to \(3x + 90 = 180\)
Now we can isolate \(x\):
\[
3x + 90 = 180
\]
Subtract 90 from both sides:
\[
3x = 90
\]
Then divide by 3:
\[
x = 30
\]
If we're asked to write the equation in the form ___x° + ___ = 180, we can rearrange it as:
\[
3x + 90 = 180
\]
So in simplest terms the answer is:
\[
3x + 90 = 180
\]
The measures of the angles are:
- m∠KLM = (x + 30)°
- m∠MLP = (2x + 60)°
Setting up the equation we have:
\[
(x + 30) + (2x + 60) = 180
\]
Now we can simplify this:
1. Combine like terms: \(x + 2x + 30 + 60 = 180\)
2. This simplifies to \(3x + 90 = 180\)
Now we can isolate \(x\):
\[
3x + 90 = 180
\]
Subtract 90 from both sides:
\[
3x = 90
\]
Then divide by 3:
\[
x = 30
\]
If we're asked to write the equation in the form ___x° + ___ = 180, we can rearrange it as:
\[
3x + 90 = 180
\]
So in simplest terms the answer is:
\[
3x + 90 = 180
\]