https://file.aiquickdraw.com/mathbot/file/17309159883864ibhb0y4.jpg

what are ​ 
𝑚
∠
1
=
m∠1=      
    degrees

​ 
𝑚
∠
2
=
m∠2=      
    degrees

​ 
𝑚
∠
3
=
m∠3=      
    degrees

​ 
𝑚
∠
4
=
m∠4=      
  degrees

​ 
𝑚
∠
5
=
m∠5=      
  degrees

To solve for the angle measures, we can use the properties of parallel lines and triangles:

1. **m∠1**: Since ∠1 and the angle marked 52° are alternate interior angles (because of the parallel lines), they are congruent.
   - **m∠1 = 52°**

2. **m∠2**: This angle is supplementary to ∠1 because they are on the same straight line.
   - **m∠2 = 180° - 52° = 128°**

3. **m∠3**: Since angles in a triangle add up to 180°, we can find m∠3 by adding the given 47° and m∠5 (which is vertically opposite to ∠3, hence m∠5 = m∠3). 

4. **m∠4**: Angle 4 is on a straight line with angle 3, making it supplementary.

Would you like the solution for each step expanded with more details? 

Here are five questions that might interest you:

1. How do parallel line properties help in finding unknown angles?
2. What is the sum of angles in any triangle, and how does it help solve problems like this?
3. How can alternate interior angles be identified?
4. What is the significance of supplementary angles on a straight line?
5. Can angles vertically opposite each other in intersecting lines be proven equal?

**Tip**: Always look for congruent angles when working with parallel lines!

What are the angle measures?

m∠1 = ______ degrees
m∠2 = ______ degrees
m∠3 = ______ degrees
m∠4 = ______ degrees
m∠5 = ______ degrees

Learn how to determine the measures of angles in a geometric configuration with parallel lines and triangles. This problem involves key geometry concepts such as the Alternate Interior Angles Theorem, Triangle Angle Sum Theorem, and properties of supplementary angles. Suitable for students in Grades 8-10.

Math Problem Statement

what are 𝑚 ∠ 1

𝑚 ∠ 2

𝑚 ∠ 3

𝑚 ∠ 4

𝑚 ∠ 5

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation