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°

Answer 1

To solve for the unknown angle measures, we start with the fact that ∠KLM and ∠MLP are supplementary angles. This means that their measures add up to 180 degrees.

Given:
- m∠KLM = (x + 30)°
- m∠MLP = (2x + 60)°

We can set up the equation based on their supplementary nature:

\[
m∠KLM + m∠MLP = 180°
\]

Substituting the expressions for the angles:

\[
(x + 30) + (2x + 60) = 180
\]

Now, we can simplify this equation:

1. Combine like terms:

\[
x + 2x + 30 + 60 = 180
\]

This simplifies to:

\[
3x + 90 = 180
\]

So the equation we can use to solve for \( x \) is:

\[
3x + 90 = 180
\]

You can write it in the form:

\[
3x + 90° = 180°
\]

Which simplifies to the simplest equation:

\[
3x = 180 - 90
\]

Thus, the simplest equation to solve for \( x \) and the angle measures is:

\[
3x = 90°
\]