Math Example--Angle Concepts--Angle Measures: Example 37

Topic

Geometry

Description

This example presents a negative angle of -195 degrees on a polar coordinate grid. The angle is marked with a red line extending from the center to a point between -180° and -210°. Students are asked to identify the angle shown, with the solution explaining that the absolute value of the angle (195°) makes it a reflex angle, and it is coterminus with 165° (calculated as 360° - 195°).

As part of a comprehensive series on angle measures, this example introduces the concept of negative reflex angles and their coterminus positive counterparts. By using a polar coordinate system, students can visualize how angles greater than 180° in the negative direction relate to their positive equivalents on the graph.

This example helps students develop a more nuanced understanding of angle measures, reinforcing the idea that angles can be represented in multiple ways. It builds upon previous examples, allowing students to see patterns in negative angles and their coterminus positive angles.

Teacher Script: "Now, class, let's examine this -195-degree angle. What does the negative sign indicate about the direction of rotation? Can you explain why we consider it a reflex angle? Let's discuss its coterminus angle of 165°. How did we calculate this? Can you think of any real-world scenarios where understanding negative reflex angles and their coterminus positive angles might be useful?"

For a complete collection of math examples related to Angle Measures click on this link: Math Examples: Angle Measures Collection.