A diagram is shown below.

Question

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

Answer 1

Since the angles \( P-Q-S \) and \( R-Q-S \) are adjacent angles that together form a straight angle at point Q, their measures must add up to 180 degrees.

Given:

• Measure of angle \( P-Q-S \) is \( x \) degrees.
• Measure of angle \( R-Q-S \) is \( x - 60 \) degrees.

The equation that represents this relationship is:

\[ x + (x - 60) = 180 \]

Now, you can solve this equation to find the measure of angle \( P-Q-S \) (which is \( x \)).

1. Combine like terms: \[ 2x - 60 = 180 \]

2. Add 60 to both sides: \[ 2x = 240 \]

3. Divide by 2: \[ x = 120 \]

Thus, the measure of angle \( P-Q-S \) is \( 120 \) degrees.