Polygons

Practice 5 items →

Convex versus concave; regular means all sides and angles equal. Students find interior and exterior angles of regular n-gons, recover n from an angle, and place quadrilaterals in the hierarchy (a square is both a rectangle and a rhombus).

Specification · for a parent or teacher

Part no.: polygons-angle-theorems
Course: High School Math 1 · Unit 14
Realm: Shapes
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

find interior and exterior angles of regular $n$ -gons; find $n$ from an angle; place a quadrilateral in the hierarchy and justify with properties.

Ready when

interior angle of a regular 12-gon, and a Venn of the parallelogram family.

Formulas

Interior sum

S = (n-2) \cdot 180^\circ

Regular interior angle

\theta = \frac{(n-2) \cdot 180^\circ}{n}

Watch for

“a square is not a rectangle”; exterior angle of regular octagon as $360/6$ .

Before · requires

Angles, triangles, and quadrilateralseuclidean-angles-polygons · Math 7

After · used by

Euclidean geometry: transformations and congruencetransformations-congruence · Math 1

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