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?

2x - 60 = 180

2x- 60 = 90

x - 60 = 90

x - 60 = 180

GPT-4o mini · Answer

To find the correct equation to solve for the measure of angle \( \angle PQS \), we first need to understand the relationship between the angles given in the problem.

We have:

\( \angle PQS = x \) degrees
\( \angle RQS = x - 60 \) degrees

Since rays \( P-Q \) and \( R-Q \) form a straight angle at point Q, the sum of these angles equals 180 degrees:

\[ \angle PQS + \angle RQS = 180 \]

Substituting the expressions for the angles, we get:

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

Now simplify this equation:

\[ x + x - 60 = 180 \]

\[ 2x - 60 = 180 \]

So the equation that can be solved to find the measure of \( \angle PQS \) (which measures \( x \) degrees) is:

\[ 2x - 60 = 180 \]

Thus, the correct answer is:

2x - 60 = 180