P, Q, and S are collinear and the measure of PQR = 120°. What does the measure of SQT have to equal to ensure that R, Q, and T are collinear?

Angles PQR and SQT are vertically opposite angles If RQT is to be a straight line (colinear).

So what should the measure of angle SQT be?

To determine the measure of angle SQT, we need to analyze the relationship between angle PQR and angle SQT.

Since P, Q, and S are collinear, the sum of angles PQR and RQS should be 180°. In other words, PQR + RQS = 180°.

We know that the measure of angle PQR is 120°, so we can substitute this value into the equation: 120° + RQS = 180°.

To find the measure of RQS, we need to isolate it by subtracting 120° from both sides of the equation: RQS = 180° - 120°.

Simplifying the equation, we get: RQS = 60°.

Therefore, the measure of angle SQT should also be 60° to ensure that R, Q, and T are collinear.

To ensure that R, Q, and T are collinear, the measure of SQT should be equal to 60°.

Here's a step-by-step explanation:

1. Given that P, Q, and S are collinear, it means that they lie on the same straight line.

2. Since the measure of PQR is given as 120°, we can conclude that the angle formed by the points Q, P, and R is 120°.

3. When three points are collinear, the sum of the measures of the adjacent angles is 180°.

4. Therefore, we can determine the measure of angle SQR by subtracting 120° from 180°: 180° - 120° = 60°.

5. To ensure R, Q, and T are collinear, the measure of the angle formed by the points Q, S, and T, which is SQT, should be equal to the measure of angle SQR.

6. Hence, the measure of SQT should be 60° in order to ensure R, Q, and T are collinear.