Cogito
Geometry · Chapter 1 · Lesson 3
Angles in Polygons
Cutting a shape into triangles.
11 problems · about 22 minutes · G-CO.C.11
What this lesson teaches
The student computes interior and exterior angle sums for any polygon.
- A polygon with n sides cuts into n − 2 triangles, so its interior sum is (n − 2) × 180°.
- Exterior angles always sum to 360°, whatever the polygon.
- A regular polygon divides either sum evenly among its corners.
Warm Up
Straightforward practice. Get the method working first.
4 problemsInterior sum of a heptagon (7 sides), in degrees?
Answer 900
Why 900°.
Interior sum of a quadrilateral, in degrees?
Answer 360
Why 2 × 180.
Interior sum of an octagon, in degrees?
Answer 1080
Why 6 × 180.
One angle of a regular octagon, in degrees?
Answer 135
Why 1080 ÷ 8.
Build It Up
The same ideas with more to keep track of.
3 problemsExterior angle sum of any polygon, in degrees?
Answer 360
Why One full turn.
One exterior angle of a regular hexagon, in degrees?
Answer 60
Why 360 ÷ 6.
Interior sum is 1440°. How many sides?
Answer 10
Why 1440 ÷ 180 = 8 triangles.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsHow many triangles does a decagon cut into?
Answer 8
Why n − 2.
Select every statement that is true for all polygons.
Answer Exterior angles sum to 360°.; It cuts into n − 2 triangles.
Why Equal angles is only true for regular polygons.
The Pentagon: Interior angle sum of a pentagon, in degrees?
Answer 540
Why 540°.
Regular Pentagon: One angle of a regular pentagon, in degrees?
Answer 108
Why 108°.