https://file.aiquickdraw.com/mathbot/file/1728557322979zi2avft9.jpg

The problem provided is asking to find the measure of angle \( \angle QTN \) in the diagram.

We can solve this by recognizing that the given lines appear to be parallel and use properties of angles formed by transversals. The angles labeled in terms of \(x\) are alternate interior angles formed by the two parallel lines and the transversal.

Here’s the breakdown:

1. The angle labeled \( (2x + 55)^\circ \) at \( \angle OST \) and the angle labeled \( (7x + 25)^\circ \) at \( \angle QTN \) are **alternate interior angles**.
   
   Since these angles are equal (due to the parallel lines and transversal), we can set them equal to each other and solve for \(x\):

   \[
   2x + 55 = 7x + 25
   \]

2. Simplify the equation:

   \[
   55 - 25 = 7x - 2x
   \]

   \[
   30 = 5x
   \]

3. Solve for \(x\):

   \[
   x = 6
   \]

4. Now, substitute \(x = 6\) back into the expression for \( \angle QTN \):

   \[
   \text{Measure of } \angle QTN = 7x + 25 = 7(6) + 25 = 42 + 25 = 67^\circ
   \]

Thus, the measure of \( \angle QTN \) is **67°**.

Would you like further clarification or more details on any part of the solution?

---

Here are five related questions:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. If the lines weren't parallel, how would that change the relationship between the angles?
3. What are the different types of angles formed when a transversal cuts two parallel lines?
4. How can you verify that two lines are parallel using angle relationships?
5. How would you solve for the measure of an angle if more than one variable is involved?

**Tip:** Always check the relationship between angles to identify if they are congruent, supplementary, or complementary when working with parallel lines and transversals.

Find the measure of \( \angle QTN \) in the diagram provided.

Learn how to find the measure of angle QTN in a diagram involving parallel lines and transversals. This problem uses the alternate interior angles theorem and requires solving a linear equation. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation