Polygon Angle Sum Formula

Show your work for each problem.

1.
What is the sum of the interior angles of a triangle?
1. a)
2. b)
3. c)
4. d)
Answer:
Using the formula: . This is the fundamental fact that the formula is based on.
2.
What is the sum of the interior angles of a quadrilateral?
1. a)
2. b)
3. c)
4. d)
Answer:
. A quadrilateral can be split into 2 triangles.
3.
What is the sum of the interior angles of a hexagon (6 sides)?
Answer: 720
4.
Into how many triangles can a pentagon be divided?
Answer: 3
A pentagon has 5 sides. triangles.
5.
What is the formula for the sum of interior angles of a polygon with sides?
1. a)
2. b)
3. c)
4. d)
Answer:
The formula is because a polygon with sides can be divided into triangles.
6.
What is the sum of the interior angles of an octagon (8 sides)?
Answer: 1080
7.
A quadrilateral has angles of , , and . What is the fourth angle?
Answer: 75
1. What is the sum of interior angles in a quadrilateral? 360
2. What is the sum of the three known angles? 285
3. Subtract the known sum from the total to find the missing angle 75
8.
What is the measure of each interior angle in a regular pentagon?
Answer: 108
Pentagon sum . Each angle
9.
What is the measure of each interior angle in a regular octagon?
Answer: 135
1. How many sides does an octagon have? 8
2. What is the sum of interior angles? Use 1080
3. Divide by 8 to find each angle 135
10.
A polygon has an interior angle sum of . How many sides does it have?
1. a)12
2. b)9
3. c)10
4. d)8
Answer: 10
, so , which means sides (decagon).
11.
A pentagon has angles of , , , and . What is the fifth angle?
Answer: 110
1. What is the total angle sum of a pentagon? 540
2. Add the four known angles 430
3. Find the missing angle 110
12.
What is the measure of each interior angle in a regular 12-sided polygon (dodecagon)?
Answer: 150
Sum . Each angle
13.
A regular polygon has interior angles of each. How many sides does it have?
Answer: 15
1. Write the equation: each angle = total sum / n, so . Multiply both sides by 156n
2. Expand the right side: 180n - 360
3. Set up equation: . Solve for 15
14.
As a regular polygon gets more and more sides, each interior angle approaches what value?
1. a)
2. b)
3. c)
4. d)
Answer:
As approaches infinity, approaches . The polygon approaches a circle with nearly straight angles.
15.
A hexagon has five angles measuring , , , , and . What is the sixth angle?
Answer: 110
1. What is the sum of interior angles of a hexagon? 720
2. Add the five known angles 610
3. Find the sixth angle 110