G.2D.1.4
G.2D.1.4 Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.
In a Nutshell
Students will explore relationships between nonoverlapping triangles formed within polygons to develop the formula for the sum and individual measure of interior angles of polygons. The concept of linear pairs is applied as it relates to the relationship between interior and exterior angles.
Student Actions

Teacher Actions


Develop a deep and flexible conceptual understanding by making the connection between linear pairs and interior and exterior angle pairs of a polygon.

Develop accurate and appropriate fluency by using efficient and accurate procedures for developing the algorithm for finding sums of interior or exterior angles and individual angle measures of a polygon through a variety of tasks.

Develop strategies for problemsolving by selecting appropriate strategies for solving modeling problems involving the interior and exterior angles of polygons and assessing the reasonableness of solutions.

Develop the Ability to Make Conjectures, Models, and Generalizations by analyzing patterns of angle relationships for various sizes of polygons to draw conclusions about the properties of interior and exterior angle sums.


Pose purposeful questions to reinforce the connection between the number of nonoverlapping triangles that can be drawn from a single vertex of a polygon to the sum of the interior angles of that polygon.

Use and connect mathematical representations by reinforcing the connection and relationship between the interior and exterior angles of a polygon and linear pairs.

Build procedural fluency by extending the concept of linear pairs to interior and exterior angles of different polygons.

Promote productive struggle by providing a variety of tasks that encourage students to prove the properties of interior and exterior angles.

Key Understandings

Misconceptions


The measures of the exterior angles of any size polygon will total 360 degrees.

The sum of the interior angles of a polygon is based on the number of nonoverlapping triangles that can be drawn from one vertex in the polygon.

The connection and relationship between interior and exterior angles if formed from linear pairs.

Each interior angle of a regular polygon has equal measures.


Students confuse interior angles and exterior angles.

Students may not correctly identify a combination of an interior and exterior angle as a linear pair and treat them as complementary instead of supplementary.

Students may forget to subtract 2 from the number of sides of a polygon before multiplying by 180 when finding the sum of interior angles.

Students correctly find the measure of one exterior angle of a polygon but may not use the linear pair relationship to find a single interior angle measure.

Students may divide the interior angle sum by the number of angles for the measure of a single interior angle with nonregular polygons.

Knowledge Connections

Prior Knowledge

Leads to



OKMath Framework Introduction
Geometry Grade Introduction
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