Math Example--Angle Concepts--Angle Measures: Example 30

Topic

Geometry

Description

This example features a negative angle of -90 degrees on a polar coordinate grid. The angle is marked in red and forms a right angle when 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 (90°) makes it a right angle, and it is coterminus with 270° (calculated as 360° - 90°).

As part of a series on angle measures, this example introduces the concept of negative right angles and their coterminus positive counterparts. By using a polar coordinate system, students can visualize how negative right angles relate to their positive equivalents on the graph.

This example helps students understand that even negative angles can form familiar angle types, reinforcing the importance of considering absolute values when classifying angles. It builds upon previous examples, allowing students to see patterns in negative angles and their coterminus positive angles.

Teacher Script: "Let's examine this -90-degree angle, class. What type of angle does it form? Can you explain why we consider it a right angle despite being negative? Now, let's discuss its coterminus angle of 270°. How might understanding negative right angles and their coterminus positive angles be useful in real-world applications, such as navigation or robotics?"

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