Understanding Exterior Angles in Convex Polygons

Objective:

Students will be able to identify and calculate exterior angles in convex polygons, as well as apply the Exterior Angle Sum Theorem to determine the total degree measure of the exterior angles.

Assessment:

Students will demonstrate mastery of the objective by correctly identifying and calculating the exterior angles of various convex polygons and explaining the application of the Exterior Angle Sum Theorem in a given task or problem.

Key Points:

• Exterior Angle: An exterior angle is an angle that is formed by extending a side of the polygon.

• Exterior Angle Sum Theorem: The Exterior Angle Sum Theorem states that the sum of the exterior angles of ANY convex polygon is 360 degrees.

• Regular Polygon Formula: If the polygon is regular with n sides, each exterior angle measures 360/n degrees.

Opening:

• Engage students by asking: "Have you ever noticed how exterior angles behave in different shapes? Let's explore why they are important in polygons."

Introduction to New Material:

• Show visual examples of convex polygons with highlighted exterior angles.

• Explain the concept of exterior angles using real-world scenarios.

• Common misconception: Students may confuse interior and exterior angles, so clarify the difference early on.

Guided Practice:

• Provide examples of convex polygons and guide students through calculating exterior angles step by step.

• Scaffold questions from simple polygons to more complex ones.

• Monitor student progress by circulating the classroom and providing immediate feedback.

Independent Practice:

• Assign a worksheet where students identify and calculate exterior angles of various convex polygons.

• Encourage students to justify their answers and show their work clearly.

• Set expectations for completion and accuracy.

Closing:

• Have students share their findings on the sum of exterior angles in different polygons.

• Summarise the importance of exterior angles in geometry.

Extension Activity:

• Challenge advanced students to explore the relationship between the number of sides in a regular polygon and the measure of each exterior angle.

Homework:

• Homework Activity: Create a poster displaying examples of convex polygons with labelled exterior angles and their measures.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.C.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.