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: \( __ = 3 \).