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 term.

__x +__ = 180

Answer 1

To find the unknown angle measures, we start with the definition of supplementary angles: two angles are supplementary if the sum of their measures equals 180 degrees.

Given:
- \( m \angle KLM = x + 30 \)
- \( m \angle MLP = 2x + 60 \)

Since these angles are supplementary, we can set up the equation:

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

Combining like terms gives us:

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

This simplifies to:

\[
3x + 90 = 180
\]

Now, to express the equation in the requested format, we want to isolate \( x \):

Subtracting 90 from both sides:

\[
3x = 180 - 90
\]

This simplifies to:

\[
3x = 90
\]

Dividing by 3:

\[
x = 30
\]

Now, referring back to the original format of the equation, we can express our equation as:

\[
x + 90 = 180
\]

Thus, the equation in simplest terms is:

\[
3x + 90 = 180
\]

Which can also be expressed as:

\[
x + 90 = 180 \quad \text{(if considering just one of the angles directly)}
\]

So, filling the blanks in the prompt you provided:

**Final Response:**

\[
\text{\_\_} x + 90 = 180
\]

**Where: \( \_\_ = 3 \)**.