If $\overline{QT}$ bisects $\angle PQR$, it divides $\angle PQR$ into two equal parts.

Given:

• $m\angle PQR = 130^\circ$
• $\overline{QT}$ bisects $\angle PQR$

To find the measure of $\angle PQT$:

1. Since $\overline{QT}$ bisects $\angle PQR$, the measure of each resulting angle will be half of $m\angle PQR$: $m\angle PQT = \frac{130^\circ}{2} = 65^\circ$

Thus, $m\angle PQT = 65^\circ$.

Would you like further details or explanations?

Here are some related questions to explore:

1. What is an angle bisector?
2. How do you construct an angle bisector geometrically?
3. What is the relationship between supplementary angles?
4. How can we apply the angle bisector theorem in triangles?
5. How can angle bisectors help in solving geometric problems?

Tip: Always remember, when a ray bisects an angle, the two resulting angles are congruent (equal in measure).