https://file.aiquickdraw.com/mathbot/file/1727717390260fxaash45.jpg

In the provided diagram, we have two parallel lines, \(q\) and \(t\), with a transversal \(r\). Angle \( \angle 1 \) is given as \(75^\circ\), and we are asked to find the sum of \( \angle 3 \), \( \angle 6 \), and \( \angle 5 \).

### Step-by-step solution:
1. **Identify relationships:**
   Since lines \(q\) and \(t\) are parallel and the transversal is \(r\), we can use the properties of corresponding angles, alternate interior angles, and supplementary angles.

2. **Determine the values of the angles:**
   - \( \angle 1 = 75^\circ \) is given.
   - Since \(q \parallel t\), \( \angle 1 \) and \( \angle 5 \) are corresponding angles. Therefore, \( \angle 5 = 75^\circ \).
   - \( \angle 3 \) and \( \angle 1 \) are vertical angles, so \( \angle 3 = 75^\circ \).
   - \( \angle 6 \) is supplementary to \( \angle 5 \) because they form a straight line. Therefore, \( \angle 6 = 180^\circ - 75^\circ = 105^\circ \).

3. **Sum of the angles:**
   Now we sum the values of \( \angle 3 \), \( \angle 6 \), and \( \angle 5 \):
   \[
   \angle 3 + \angle 6 + \angle 5 = 75^\circ + 105^\circ + 75^\circ = 255^\circ
   \]

### Final answer:
The sum of \( \angle 3 \), \( \angle 6 \), and \( \angle 5 \) is \( 255^\circ \).

---

Would you like more details on how the relationships between angles work?

Here are 5 related questions to deepen your understanding:
1. What are alternate interior angles, and how can they help in solving parallel line problems?
2. How do vertical angles relate to each other?
3. Can you find the value of \( \angle 4 \) in this diagram?
4. How do corresponding angles work when two parallel lines are cut by a transversal?
5. What is the significance of supplementary angles in geometry?

**Tip**: When dealing with parallel lines and a transversal, always look for corresponding and alternate interior angles as these often provide key angle measures.

Line q and line t are parallel, and angle 1 is 75 degrees. Find the sum of angles 3, 6, and 5.

Learn how to find the sum of angles 3, 6, and 5 when two parallel lines are cut by a transversal. The problem uses key geometry concepts such as corresponding, vertical, and supplementary angles to arrive at a solution. Perfect 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