Classifying 2D Shapes — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is the sum of interior angles in a hexagon?
A) 540°
B) 720°
C) 900°
D) 1080°
A hexagon has 6 sides, so its interior angle sum is (6 - 2) x 180° = 4 x 180° = 720°.
2. A regular polygon has each interior angle measuring 135°. How many sides does it have?
A) 6
B) 7
C) 8
D) 10
Each exterior angle is 180° - 135° = 45°, and since exterior angles sum to 360°, dividing 360° / 45° = 8 sides, making it a regular octagon.
3. Which of these shapes always has perpendicular diagonals?
A) Rectangle
B) Parallelogram
C) Rhombus
D) Trapezoid
A rhombus always has diagonals that cross at right angles (90°), which is a defining property that sets it apart from other quadrilaterals like rectangles or general parallelograms.
4. A convex polygon has 5 sides. One of its angles is missing. The other four angles are 100°, 110°, 120°, and 95°. What is the missing angle?
A) 105°
B) 115°
C) 125°
D) 135°
A pentagon's angles sum to 540°. Adding the four known angles gives 100° + 110° + 120° + 95° = 425°, so the missing angle is 540° - 425° = 115°.
Part B: Fill in the Blank
Write the correct answer on each line.
1. Each interior angle of a regular decagon measures 144 degrees.
A regular decagon has an angle sum of (10 - 2) x 180° = 1440°, and dividing by 10 equal angles gives 1440° / 10 = 144° each.
2. A polygon with all sides and all angles equal is called a regular polygon.
When every side has the same length and every angle has the same measure, the polygon meets the definition of a regular polygon.
3. The number of triangles formed by drawing all diagonals from one vertex of a hexagon is 4.
Drawing diagonals from one vertex of a hexagon divides it into (6 - 2) = 4 non-overlapping triangles, which is also how the angle-sum formula works.
4. A regular pentagon has interior angles of 108° each and 5 lines of symmetry.
A regular polygon has as many lines of symmetry as it has sides, so a regular pentagon with its five equal sides has exactly 5 lines of symmetry.
5. The sum of exterior angles of any convex polygon is always 360 degrees.
No matter how many sides a convex polygon has, its exterior angles always add up to 360° because walking around the perimeter brings you full circle.