https://file.aiquickdraw.com/mathbot/file/172766952132592xt0y50.jpg

We are given that lines \( m \) and \( n \) are parallel, and we need to find the measure of each numbered angle in the diagram.

Looking at the image:
- Angle \( \angle 3 \) is given as \( 76^\circ \),
- Angle \( \angle 8 \) is given as \( 121^\circ \).

Now, to find \( \angle 1 \), we can use the following steps:

### Step 1: Use the concept of alternate interior angles
Since \( m \parallel n \), and angles \( 1 \) and \( 8 \) are alternate interior angles, they must be congruent. Therefore,
\[
\angle 1 = \angle 8 = 121^\circ.
\]

Thus, 
\[
m\angle 1 = 121^\circ.
\]

Would you like further details on this, or do you have any questions? 

Here are 5 related questions that expand on this:

1. How can we use vertical angles to find other angles in this diagram?
2. What are the corresponding angles, and how can they help solve for other unknowns?
3. How do we use the sum of angles in a straight line to find unknown angles?
4. Can you identify another pair of alternate interior angles in the diagram?
5. How can we find the measure of angles 2 and 4?

**Tip:** When working with parallel lines, always look for alternate interior angles, corresponding angles, and vertical angles for solving unknowns efficiently.

In this exercise, lines m and n are parallel. Find the measure of each numbered angle. What is the measure of ∠1?

This problem demonstrates how to find the measure of numbered angles when lines m and n are parallel, using alternate interior angles. Learn how to solve for ∠1, which is congruent to ∠8, based on the Alternate Interior Angles Theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation