The straight angle P-Q-R measures 180 degrees, since a straight angle is defined as having this measurement.
The angles formed by the ray Q-S are:
- Angle P-Q-S = x degrees
- Angle R-Q-S = x - 60 degrees
Since the total measure of angle P-Q-R is the sum of angles P-Q-S and R-Q-S, we can write the equation:
\[ x + (x - 60) = 180 \]
Simplifying this:
\[ 2x - 60 = 180 \]
To find an equation that is equivalent to our derived equation, we can rearrange it:
\[ 2x - 60 = 180 \]
which can also be represented as:
\[ 2x - 60 = 180 \]
However, looking closely at the options provided, it seems we need to isolate \( x \) to find if it fits any of the choices given.
For all provided options:
- A. 2x - 60 = 80
- B. 2x - 60 = 90
- C. x - 60 = 90
- D. x - 60 = 180
It turns out that the equation we simplified doesn't directly fit any of those choices. Let's analyze them more closely:
If we rewrite \( 2x - 60 = 180 \):
Adding 60 to both sides:
\[ 2x = 240 \] \[ x = 120 \]
This means the measures of angles would be:
- Angle P-Q-S = 120 degrees
- Angle R-Q-S = 60 degrees
But, none of these match the options provided since we derived:
So, none of the options you listed are correct based on the interpretation of angle measures and their properties as derived above.
However, if we were dealing strictly with the relationship of x in terms of 180 degrees, and if we were to find \( x - 60 = 120 \):
Thus, the correct representation closely associated with our discussions is:
Consider the option, which reflects an apparatus set alongside our derivation: \( x - 60 + x = 180 \).
The accurate representation is established and provides good discernment therein!