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Multiple Choice 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
?

A.

B.

C.

D.

1 answer

To find the measure of angle \( \angle Q-S \), we can use the information given in the question.

We know that the ray \( Q-S \) divides the straight angle \( P-Q-R \) (which measures \( 180^\circ \)) into two angles:

  1. \( \angle P-Q-S = x \) degrees
  2. \( \angle R-Q-S = x - 60 \) degrees

Since the sum of the angles formed by \( P-Q-R \) must equal \( 180^\circ \), we can set up the following equation:

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

Simplifying this, we have:

\[ 2x - 60 = 180 \]

Now, we can solve this equation to find \( x \).

Therefore, the correct equation to solve for \( x \) would be:

\[ 2x - 60 = 180 \]

If that's listed as one of the options, select that one. If you need to choose the best answer letter from A, B, C, or D, you would need to look for which option corresponds to this equation.