Question
A diagram is shown below.
The ray Q-S divides a straight angle P-Q-R into angle P-Q-S measuring x degrees and angle R-Q-S measuring x minus 60 degrees.
Which equation can be solved to find the measure in degrees of PQS
?
A. 2x-60=180
B. 2x-60=90
C. z-60=90
D. x-60=180
The ray Q-S divides a straight angle P-Q-R into angle P-Q-S measuring x degrees and angle R-Q-S measuring x minus 60 degrees.
Which equation can be solved to find the measure in degrees of PQS
?
A. 2x-60=180
B. 2x-60=90
C. z-60=90
D. x-60=180
Answers
GPT-4o mini
To find the equation that can be solved to find the measure of angle P-Q-S (PQS), we start with the information given about the angles.
According to the problem:
- Angle P-Q-S (PQS) measures \( x \) degrees.
- Angle R-Q-S measures \( x - 60 \) degrees.
- The ray Q-S divides the straight angle P-Q-R into these two angles, meaning the sum of these angles must equal 180 degrees (since a straight angle measures 180 degrees).
We can set up the equation based on this relationship:
\[
x + (x - 60) = 180
\]
Now, simplify the left side:
\[
x + x - 60 = 180
\]
\[
2x - 60 = 180
\]
Thus, the correct equation to solve for \( x \) is:
\[
2x - 60 = 180
\]
The correct answer is:
**A. 2x - 60 = 180**
According to the problem:
- Angle P-Q-S (PQS) measures \( x \) degrees.
- Angle R-Q-S measures \( x - 60 \) degrees.
- The ray Q-S divides the straight angle P-Q-R into these two angles, meaning the sum of these angles must equal 180 degrees (since a straight angle measures 180 degrees).
We can set up the equation based on this relationship:
\[
x + (x - 60) = 180
\]
Now, simplify the left side:
\[
x + x - 60 = 180
\]
\[
2x - 60 = 180
\]
Thus, the correct equation to solve for \( x \) is:
\[
2x - 60 = 180
\]
The correct answer is:
**A. 2x - 60 = 180**