Exploring Interior Angles in Convex Polygons

Objective:

Students will be able to calculate interior angles in convex polygons using the Polygon Sum Formula and the equiangular polygon angle measure formula.

Assessment:

Students will be given a worksheet with various convex polygons where they need to calculate the interior angles using the formulas provided. This assessment will measure their ability to apply the Polygon Sum Formula and the equiangular polygon angle measure formula accurately.

Key Points:

• The interior angle of a polygon is an angle inside the shape.

• A polygon has the same number of interior angles as it has sides.

• The Polygon Sum Formula states that for any n-gon, the sum of interior angles is equal to (n-2) x 180.

• For any equiangular n-gon, each angle's measure is [(n-2) x 180]/n.

Opening:

• Engage students with a visual of different polygons and ask: "How are the interior angles of polygons related to the number of sides they have?"

Introduction to New Material:

• Present key points through examples and visuals.

• Common misconception: Students may mistakenly believe that the interior angles of polygons are always the same.

Guided Practice:

• Work through examples together, starting with simple polygons and gradually increasing complexity.

• Monitor student understanding by asking questions as students work through practice problems.

Independent Practice:

• Assign a worksheet where students calculate interior angles of various convex polygons using the Polygon Sum Formula and the equiangular polygon angle measure formula.

• Remind students of the importance of showing their work and reasoning clearly.

Closing:

• Have students share their answers and discuss any common challenges faced during the independent practice.

• Summarise key learnings about interior angles in convex polygons.

Extension Activity:

• Task early finishers with creating their own convex polygon and calculating its interior angles using the formulas learned.

Homework:

• For homework, students could research real-life applications of understanding interior angles in polygons, such as architecture or design projects.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.C.9 - Prove theorems about lines and angles.

• CCSS.MATH.CONTENT.HSG.CO.C.9 - Derive the formula for the sum of the interior angles of a polygon, where n is the number of sides of the polygon.