To determine which ray is between the other two, we can analyze the measures of the angles involved.
We know:
- m∠RSQ = 35°
- m∠QST = 50°
- m∠RST = 85°
Since point Q lies in the interior of angle ∠RST, we can apply the property of angle addition. The measure of angle ∠RST can be found by adding the measures of angles ∠RSQ and ∠QST:
\[ m∠RST = m∠RSQ + m∠QST \] \[ m∠RST = 35° + 50° = 85° \]
This matches the given m∠RST = 85°, confirming our angle measures are correct.
Now we can determine the relative positions of rays SQ, SR, and ST. We note that m∠RSQ (35°) is less than m∠QST (50°), which suggests that ray SQ is closer to ray SR. Therefore, ray SQ lies between ray SR and ray ST.
So, the ray that is between the other two is:
Ray SQ.