Math Example--Angle Concepts--Angle Measures: Example 35

Topic

Geometry

Description

This example showcases a negative angle of -165 degrees on a polar coordinate graph. The angle is marked in red and measured clockwise from the positive x-axis. Students are asked to identify the angle shown, with the solution explaining that the absolute value of the angle (165°) makes it an obtuse angle, and it is coterminus with 195° (calculated as 360° - 165°).

As part of a comprehensive series on angle measures, this example further explores the concepts of negative obtuse angles and their coterminus positive counterparts. By using a polar coordinate system, students can visualize how angles 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 -165-degree angle. How does it compare to the previous negative angles we've studied? Can someone explain why we still consider it an obtuse angle despite being close to a straight angle? Let's discuss its coterminus angle of 195°. How did we calculate this? Can you think of any practical applications where understanding negative obtuse angles and their coterminus positive angles might be useful in fields like architecture or engineering?"

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