https://file.aiquickdraw.com/mathbot/file/1727291263602ty2nbw1d.jpg

In the given diagram, lines A and B are parallel, and the angle labeled as 141° is an exterior angle. The angle \( \angle a \) and the 141° angle are *same-side exterior angles* or *consecutive exterior angles*, which are supplementary since they lie on the same side of the transversal.

To find \( m \angle a \), we can use the property of supplementary angles:

\[
m \angle a + 141^\circ = 180^\circ
\]

\[
m \angle a = 180^\circ - 141^\circ
\]

\[
m \angle a = 39^\circ
\]

Thus, the measure of \( \angle a \) is \( 39^\circ \).

Would you like a further breakdown or more details on the reasoning? Here are some additional related questions:

1. What are supplementary angles?
2. How do you identify same-side exterior angles in parallel lines?
3. Why are same-side exterior angles supplementary?
4. What other angles can be formed by a transversal intersecting parallel lines?
5. Can you name another pair of supplementary angles from this diagram?

**Tip:** When dealing with parallel lines, remember that same-side exterior and interior angles are always supplementary!

Lines A and B are parallel. Find the measure of angle a.

Learn how to find the measure of an angle formed by two parallel lines and a transversal. This problem uses the same-side exterior angles theorem and supplementary angle properties to determine that the measure of angle a is 39°. 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