Solving Problems involving Sides and Angles of a Polygon

1. Solving Problems involving Sides and
Angles of a Polygon
Enhancement and Consolidation Camps

2. Lesson Component 1 (Lesson Short Review)
Time: 7 minutes
Questions
Key Idea: Solving Problems involving Sides and Angles of a Polygon.
1. (i) Complete: A polygon with equal sides and equal interior angles is
called a ………. polygon.
(ii) Complete: An interior angle and associated exterior angle of a
polygon add to ………. degrees
regular
180

3. Lesson Component 1 (Lesson Short Review)
Time: 7 minutes
Questions
Key Idea: Solving Problems involving Sides and Angles of a Polygon.
2. Use the formula: Measure of exterior angle of regular polygon = 360°
𝑛𝑛 , where 𝑛𝑛 is the number of sides of the polygon, to find the size of
the exterior angles of:
(i) an equilateral triangle.
(ii) a regular nonagon (9-sided polygon)
120°
40°

4. Lesson Component 1 (Lesson Short Review)
Time: 7 minutes
Questions
Key Idea: Solving Problems involving Sides and Angles of a Polygon.
3. The exterior angles of a regular dodecagon (12-sided polygon) are
each 30°.
Use this information to calculate the sum of the interior angles of a
dodecagon
1800°

5. corresponding, dodecagon/nonagon/octagon, exterior angle, formula, interior angle, property,
regular polygon
Lesson Component 3 (Lesson Language Practice)
Time: 5 minutes
Direction: Choose the correct word that corresponds to the following statements.
1. _____________________angles are two angles in the same relative position on two lines
when those lines are cut by a transversal.
2. _____________________ a pair of parallel lines that are intersected with a transversal.
3. _____________________is an equation or rule that shows a relationship between two or
more numbers.
4. _____________________angle at a vertex of a polygon, the angle that lies between the
polygon.
5. _____________________is a polygon in which all the angles are equal and all of the sides
are equal.
6. _____________________is a twelve sided polygon.
7. _____________________is a nine sided polygon.
8. _____________________is a polygon with eight sides.
corresponding
exterior angle
formula
interior angle
regular polygon
dodecagon
nonagon
octagon

6. Lesson Component 4 (Lesson Activity)
Time: 25 minutes
Part 4A

7. Key Idea: Solving Problems involving Sides and Angles of a Polygon.
Questions:
1. Matthew observes that Triangle 1 and Triangle 6 have two sides
each that are sides of the octagon.
(i) By considering their sides, what type of triangle must Triangle 1 and
Triangle 6 be?
(ii) How many pairs of equal corresponding sides and angles do Triangle
1 and Triangle 6 have?
isosceles
three pairs of corresponding sides and three pairs of corresponding
angles
Part 4B

8. 2. Matthew knows the formula:
Measure of exterior angle of regular polygon = 360° 𝑛𝑛 , where 𝑛𝑛 is the
number of sides of the polygon.
(i) The angle marked 𝑎𝑎° in the diagram is one of the exterior angles of
the octagon. Use the formula to show that 𝑎𝑎° = 45°.
(ii) Each of the six equal angles that meet at 𝐴𝐴 is an angle of each of
Triangles 1 to 6. By first determining the size of each interior angle of the
octagon using the result in 2(i), find the size of each of the six angles.
Exterior angle of octagon =360° 8
= 45°
Interior angle of octagon = 180° − 45° = 135°
Size of six equal angles that meet at 𝐴𝐴 = 135° 6 = 22.5°

9. 3. (i) Using the size of each interior angle found in 2(ii), show that the
sum of the interior angles of the octagon is 1080°.
(ii) How could Matthew have found the sum of the interior angles of the
octagon, without knowing the size of each interior angle, immediately
following the construction of his diagram?
Sum of the interior angles = 8 × 135°
= 1080°
Sum of the interior angles = angle sum of the six triangles that form the octagon
= 6 × 180° = 1080°

10. Key Idea: Solving Problems involving Sides and Angles of a Polygon.
Questions:
1. Triangle 3 is a right-angled triangle. If the diagonal 𝐴D of the octagon
is approximately 4.8 meters long, find the area of Triangle 3.
2. Using the fact that Triangle 3 is right-angled and results found in 2(ii)
of Part 4B, calculate the size of the obtuse angle in Triangle 2.
Area of Triangle 3 ≅ 28.8 𝑚2
Size of obtuse angle in Triangle 2 = 112.5°
Part 4C

11. Key Idea: Solving Problems involving Sides and Angles of a Polygon.
3. The formula that is used to find the number of diagonals in any
polygon is:
Number of diagonals = 1 2 × 𝑛𝑛 × (𝑛𝑛 − 3), where '𝑛𝑛' represents the
number of sides of the polygon.
(i) Use the formula to find the number of diagonals that Matthew could
draw in the octagon.
(ii) What fraction of the number of possible diagonals did Matthew draw
when he divided the octagon into 6 triangles?
20
1
4
Part 4C

12. .
Lesson Component 5 (Lesson Conclusion – Reflection/Metacognition on
Student Goals)
Time: 5 minutes
o What do you think were the key mathematical concepts addressed in this
lesson?
o Would you rate your level of understanding of the material covered in this
lesson as high, moderate, or low?
o Has the lesson helped you gain further insight into aspects of the material
covered that represent strengths or represent weaknesses?

13. .
Lesson Component 5 (Lesson Conclusion – Reflection/Metacognition on
Student Goals)
Time: 5 minutes
o What would you describe as the main barriers, if any, to your ongoing
progress and achievement in relation to the topic area addressed in this
lesson?
o What do you think would best assist your ongoing progress and achievement
in relation to the topic area?