Florida B.E.S.T. MA.8.GR.1.6
The Standard
Develop and use formulas for the sums of the interior angles of regular polygons by decomposing them into triangles.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw diagonals from one vertex to split a polygon into nonoverlapping triangles. They connect n sides to n − 2 triangles and calculate the total interior angle measure with (n − 2) × 180°. For a regular polygon, they can divide that total by n to find one interior angle.
What Mastery Looks Like
- Given any regular polygon, a student identifies n, calculates (n − 2) × 180°, and labels the result as the interior angle sum. The student can sketch a valid triangulation and explain why the triangle count is two less than the number of sides.
Common Misconceptions
- Students may count n triangles by drawing from the center, then multiply by 180° without subtracting the angles around the center. They may use n − 1 instead of n − 2, or confuse the total angle sum with one interior angle. Some count overlapping triangles created by too many diagonals.
How to Assess It
- Exit ticket: Draw a triangulation of a regular decagon, then use it to find the sum of the interior angles and explain your formula.
Lesson moves
Ways to Teach It
Give students paper pentagons, hexagons, and octagons to draw diagonals from one vertex, cut out the triangles, and record the angle sums.
Ask students to explain in writing why an n-sided polygon makes n − 2 triangles when all diagonals begin at one vertex.
Make card sets showing polygon diagrams, side counts, triangle counts, and angle sums, then have pairs race to build correct matches.
Show an octagonal gazebo floor plan and have students calculate the total of its corner angles and each equal corner angle.
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Printable MA.8.GR.1.6 Worksheet
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Related Standards
- MA.6.GR.2.2
Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.
- MA.7.GR.1.2
Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
- MA.8.GR.1
Develop an understanding of the Pythagorean Theorem and angle relationships involving triangles.
- MA.8.GR.1.5
Solve problems involving the relationships of interior and exterior angles of a triangle.
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