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 angles ∠KLM and ∠MLP are supplementary, their measures add up to 180°. We can set up the equation using the given expressions for the angles:
\[
m∠KLM + m∠MLP = 180°
\]
Substituting the measures of the angles:
\[
(x + 30) + (2x + 60) = 180°
\]
Now, combine like terms:
\[
x + 30 + 2x + 60 = 180°
\]
This simplifies to:
\[
3x + 90 = 180°
\]
Thus, the equation in its simplest terms is:
\[
3x + 90 = 180°
\]
So, filling in the blanks for your template:
**3x° + 90° = 180°**
\[
m∠KLM + m∠MLP = 180°
\]
Substituting the measures of the angles:
\[
(x + 30) + (2x + 60) = 180°
\]
Now, combine like terms:
\[
x + 30 + 2x + 60 = 180°
\]
This simplifies to:
\[
3x + 90 = 180°
\]
Thus, the equation in its simplest terms is:
\[
3x + 90 = 180°
\]
So, filling in the blanks for your template:
**3x° + 90° = 180°**