Unit 8 - Day 1

Interior and Exterior Angles

Unit 8 - Lesson 1

Interior and Exterior Angles

Unit 8 - Day 1

Learning Objectives:

At the end of today's session, you should be able to:

• Identify and define the interior and exterior angles of various polygons.

• Calculate the measure of interior and exterior angles for regular polygons using appropriate formulas.

• Apply their knowledge of interior and exterior angles to solve different geometric problems

Reminder:

This is a daily graded activity as part of your PARTICIPATION GRADE:

Make sure to finish both Quizizz and paper work. When done, you have to submit your paper for checking. This is individual graded activity but feel free to work with your peers if necessary. Simply raise your hand for questions and clarifications.

Polygon

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A polygon is closed figure formed by 3 or more line segments called sides.

Categorize

Options (7)

Polygon or Not

Polygons

Not Polygons

In the figure, numbers 1,3,4,7,10 are polygon because these are CLOSED FIGURES with STRAGITH SIDES. While numbers 2, 6 & 9 are not because of the curve sides and 5 & 8 are not closed figures.

Clarification:

Sum of the Interior Angle Measures

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The sum of the measures of the interior angles can be determined by the number of triangles that can be drawn within the polygon.

Analyze the table below...
What pattern can you make out of this in finding the sum of the interior angles of a polygon!

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Multiple Select

Which of the following is/are TRUE about the table?

• The difference between the number of sides and the number of triangles is always 2.

• The difference between the sum of interior angles is 180 degrees?

• The formula in getting the sum of interior angles is 180(n-2) which means for a triangle,
  Sum of int. <'s = 180(3-2)
  Sum of int. <'s = 180 (1)
  Sum of int. <'s = 180⁰

• The formula in getting the sum of interior angles is 180(n-2) which means for a hexagon,
  Sum of int. <'s = 180(5-2)
  Sum of int. <'s = 180 (3)
  Sum of int. <'s = 720⁰

Drag and Drop

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No. of Triangles = ​ ​

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Sum of interior angles = ​

​

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7

5

900 degrees

6

4

720 degrees

1080 degrees

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No. of Triangles = ​ ​

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Sum of interior angles = ​ ​

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8

5

900 degrees

6

4

720 degrees

1080 degrees

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No. of Triangles = ​ ​

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Sum of interior angles = ​

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9

10

1060 degrees

7

8

1160 degrees

1260 degrees

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No. of Triangles = ​ ​

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Sum of interior angles = ​

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9

10

1240 degrees

11

8

1340 degrees

1440 degrees

Interior Angle Sum Formula

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If n represents the number of sides of a polygon, then the sum of the interior angle, S, can be found using the formula:


S = 180 ( n - 2)

Interior Angle Sum Formula

Examples:

S = 180 ( n - 2)

Pentagon, n = 5 sides
S = 180 (n - 2)
S = 180 (5 - 2)
S = 180 (3)
S = 540 degrees

Nonagon, n = 9 sides
S = 180 (n - 2)
S = 180 (9 - 2)
S = 180 (7)
S = 1260 degrees

Dropdown

Complete the solution for the following:

15-gon, meaning 15-sided polygon



S = 180 (n-2)

S = 180 (​

Select answer

- 2)

S = 180 (​

Select answer

)

S = ​

Select answer

Make sure to put this on your notes!

Dropdown

Complete the solution for the following:

21-gon, meaning a polygon with 21 sides



S = 180 (n-2)

S = 180 (​

Select answer

- 2)

S = 180 (​

Select answer

)

S = ​

Select answer

Make sure to put this on your notes!

Dropdown

Complete the solution for the following:

21-gon, meaning a polygon with 48 sides



S = 180 (n-2)

S = 180 (​

Select answer

- 2)

S = 180 (​

Select answer

)

S = ​

Select answer

Make sure to put this on your notes!

Dropdown

Complete the solution for the following:

21-gon, meaning a polygon with 36 sides



S = 180 (n-2)

S = 180 (​

Select answer

- 2)

S = 180 (​

Select answer

)

S =

Select answer

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Regular Polygons

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A polygon in which all sides measures are CONGRUENT, therefore all angle measures are also CONGRUENT.

Interior Angles of a
Regular Polygons

Examples:

Regular Quadrilateral, n = 4
Sum of interior = 360⁰ (refer to your notes if not sure)

Int. <'s of Regular Quadrilateral = 360 / 4
Int <'s of Regular = 90⁰

Sum of interior
no. of sides

Interior Angles of a
Regular Polygons

Examples:

Regular Hexagon, n = 6
Sum of interior = 720⁰ (refer to your notes if not sure)

Int. <'s of Regular Quadrilateral = 720 / 6
Int <'s of Regular = 120⁰

Sum of interior
no. of sides

Interior Angles of a
Regular Polygons

Examples:

Regular Nonagon, n = 9
Sum of interior = 1260⁰ (refer to your notes if not sure)

Int. <'s of Regular Quadrilateral = 1260 / 9
Int <'s of Regular = 140⁰

Sum of interior
no. of sides

Dropdown

Complete the solution for the following:

Regular PENTAGON has 5 equal sides and 5 equal angles.



Sum of interior angles of a pentagon = ​ ​ 540



Interior Angles of a Regular Pentagon = ​

Select answer

/ ​

Select answer

Interior Angles of a Regular Pentagon = ​

Select answer

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Dropdown

Complete the solution for the following:

Regular 18-GON has 18 equal sides and 18 equal angles.



Sum of interior angles of a 18-gon = ​ ​ 180 (​

Select answer

-2)

Sum of interior angles of a 18-gon = 180 (​

Select answer

)

Sum of interior angles of an 18-gon = ​

Select answer

Now divide your sum of interior and 18

therefore,

Interior Angles of a Regular Pentagon = ​

Select answer

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Sum of Interior Angles Measures

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Exterior angles are supplementary, meaning forms 180 degrees, to their adjacent interior angle. Find the measure of each exterior angle on the polygons below, then give the sum of all exterior angle measures

<--Supplementary means, this interior and exterior angle must form 180 degrees together!

?

O

O

Multiple Choice

So what is the angle supplementary to 40⁰?

• 101⁰

• 119⁰

• 140⁰

• 160⁰

<--Supplementary means, this interior and exterior angle must form 180 degrees together!

?

O

O

Multiple Choice

So what is the angle supplementary to 79⁰?

• 101⁰

• 119⁰

• 140⁰

• 111⁰

Supplementary means, this interior and exterior angle must form 180 degrees together! -->

?

O

O

Multiple Choice

So what is the angle supplementary to 61⁰?

• 101⁰

• 119⁰

• 140⁰

• 129⁰

Multiple Choice

What about the sum of the 3 exterior angles:

• 300⁰

• 360⁰

• 180⁰

• 240⁰

Drag and Drop

Find the supplementary angles of the following based on the figure.



124⁰ is supplementary with ​

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71⁰ is supplementary with ​

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89⁰ is supplementary with ​

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76⁰ is supplementary with​ ​

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56 degrees

109 degrees

91 degrees

104 degrees

66 degrees

119 degrees

101 degrees

94 degrees

114 degrees

Multiple Choice

What about the sum of the 4 exterior angles:

• 300⁰

• 360⁰

• 320⁰

• 340⁰

Drag and Drop

Find the supplementary angles of the following based on the figure.



98⁰ is supplementary with ​

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104⁰ is supplementary with ​

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130⁰ is supplementary with ​

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87⁰ is supplementary with​ ​

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121⁰ is supplementary with​ ​​

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82 degrees

86 degrees

50 degrees

93 degrees

92 degrees

70 degrees

76 degrees

69 degrees

83 degrees

59 degrees

Multiple Choice

What about the sum of the 5 exterior angles:

• 300⁰

• 360⁰

• 280⁰

• 240⁰

Drag and Drop

Find the supplementary angles of the following based on the figure.



129⁰ is supplementary with ​

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115⁰ is supplementary with ​

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117⁰ is supplementary with ​

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123⁰ is supplementary with​ ​

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112⁰ is supplementary with​ ​​

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124⁰ is supplementary with​ 56 degrees

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51 degrees

65 degrees

63 degrees

57 degrees

62 degrees

64 degrees

69 degrees

68 degrees

Multiple Choice

What about the sum of the 6 exterior angles:

• 340⁰

• 360⁰

• 380⁰

• 320⁰

What can you conclude about the sum of the exterior angles measures of a polygon?

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Drag and Drop

How many sides does a regular hexagon has? ​

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What is the sum of the exterior angles of a polygon?​

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To find the answer, divide 360 by the number of sides which is equal to ​

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180 degrees

7 sides

6 sides

360 degrees

60 degrees

120 degrees

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How many sides does a regular 24-gon has? ​

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What is the sum of the exterior angles of a polygon?​

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To find the answer, divide 360 by the number of sides which is equal to ​

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180 degrees

12 sides

24 sides

360 degrees

15 degrees

12 degrees

Drag and Drop

If exterior angle is 12⁰, let's find out first how many sides does it have.
Remember the formula in finding the exterior angle is

360 / no. of sides = 12⁰

So to simply find the number of sides, we just divide 360 again but this time, by the exterior angle which is 12⁰.

So what is 360/12?

​ ​

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12 sides

15 sides

30 sides

Drag and Drop

If exterior angle is 40⁰, let's find out first how many sides does it have.
Remember the formula in finding the exterior angle is

360 / no. of sides = 40⁰

So to simply find the number of sides, we just divide 360 again but this time, by the exterior angle which is 40⁰.

So what is 360/40?

​ ​

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and what do we call the 9-sided polyon?
​

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12 sides

8 sides

9 sides

nonagon

decagon

octagon

Finding exterior angles and no. of sides for a regular polygon.

Make sure to write this formula on your notes!

Reminder:

This is a daily graded activity as part of your PARTICIPATION GRADE:

You are now done with Quizizz but make sure to finish your notes as well. When done, you have to turn in your paper for checking. This is individual graded activity but feel free to work with your peers if necessary.
Work on the homework assigned in this lesson!
Check it from DELTA Math website or through your google classroom!