Suppose m™PQR = 130°. If QTÆ˘ bisects ™PQR, what is the measure 

of ™PQT?

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).

Suppose m∠PQR = 130°. If QT bisects ∠PQR, what is the measure of ∠PQT?

Discover how to find the measure of angle PQT when QT bisects angle PQR, given that m∠PQR = 130°. Learn how to apply the concept of angle bisectors and use basic geometry formulas. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation