Classifying 2D Shapes — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The sum of interior angles in a pentagon is 540 degrees.
Using the formula (n - 2) x 180°, a pentagon (5 sides) gives (5 - 2) x 180° = 3 x 180° = 540°.
2. Each interior angle of a regular hexagon measures 120 degrees.
A regular hexagon has an angle sum of (6 - 2) x 180° = 720°, and dividing equally among 6 angles gives 720° / 6 = 120° per angle.
3. A polygon with ten sides is called a decagon.
The prefix "deca" means ten, so a ten-sided polygon is called a decagon.
4. The formula for the sum of interior angles of a polygon is (n − 2) × 180 degrees.
The formula works because any polygon can be divided into (n - 2) triangles from one vertex, and each triangle contains 180°.
5. A regular polygon with all angles equal to 108° has 5 sides.
If each interior angle is 108°, the total angle sum is found by working backward: 180° - 108° = 72° exterior angle, and 360° / 72° = 5 sides, making it a regular pentagon.
6. The sum of interior angles in an octagon is 1080 degrees.
An octagon has 8 sides, so the angle sum is (8 - 2) x 180° = 6 x 180° = 1080°.
7. A polygon is convex if all its interior angles are less than 180°.
A convex polygon has every interior angle less than 180°, which means no part of the shape "caves in" — if any angle exceeded 180°, the polygon would be concave.
8. Each interior angle of a regular triangle (equilateral) measures 60 degrees.
An equilateral triangle has three equal angles, and since the total is 180°, each angle measures 180° / 3 = 60°.
9. A polygon that has at least one angle greater than 180° is called concave.
When at least one interior angle exceeds 180°, part of the polygon "caves inward," which is why it is called concave — the opposite of convex.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each polygon to its interior angle sum.
Triangle (3 sides)
→ 180°
540°
Quadrilateral (4 sides)
→ 360°
360°
Pentagon (5 sides)
→ 540°
720°
Hexagon (6 sides)
→ 720°
180°
Correct matches: Triangle (3 sides) → 180°; Quadrilateral (4 sides) → 360°; Pentagon (5 sides) → 540°; Hexagon (6 sides) → 720°.