∠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:

\[ 3x = 90° \]