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Confidential 2

In the given figure 1, AB || CD and AC || BD

1) Find x Answer= 40°

2) Find y Answer= 35°

In the given figure 2, l || m

3) Find x Answer= 135°

4) Find y Answer= 135°

5) Find z Answer= 45°

6) Find w Answer= 45°

Figure 1

Figure 2

Warm up

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Parallel lines are two lines in a plane which do not meet even when produced indefinitely.

When a transversal cuts two parallel lines pairs, the sum of the interior angles on the same side of transversal is 180°.

When a transversal cuts two parallel lines pairs of corresponding angles are equal.

When a transversal cuts two parallel lines pairs of alternate interior angles are equal.

Lets recap what we have learned in the previous lesson

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Two lines are parallel if any one of the following conditions hold:

• Pairs of alternate interior angles are equal.

• Pairs of corresponding angles are equal.• The sum of the interior angles on the

same side of transversal is 180°

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Let’s get startedPolygon: A polygon is a closed plane figure

with three or more sides that are all straight. The sides do not cross each other. Two sides meet at every vertex.

Examples:

1. Triangle

2. Rectangle

3. Square

4. Pentagon

5. Hexagon

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Types of Polygons

Concave polygon

Convex polygon

Regular polygon

Irregular polygon

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Concave polygon

If a polygon has a reflex angle (A reflex angle isgreater than 180º and less than 360º) then it is saidto be a concave polygon.

Example:

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Convex polygon

A polygon that has all interior angles less than 180°.Every line segment between two vertices of thepolygon does not go exterior to the polygon.

Example:

Regular pentagon

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Regular polygon

A regular polygon's sides are all of the same length

and its angles are the same size. Examples:

Square

Equilateral Triangle

Regular hexagon

Regular octagon

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Irregular polygon

If a polygon is not a regular polygon, then it is saidto be an irregular polygon.

Example:

Quadrilateral

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Names of Polygons

Name Sides

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

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Triangle

Quadrilateral Family

Pentagon

Rectangle Square

Parallelogram Trapezium

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Hexagon Heptagon Octagon

Nonagon

Decagon

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Diagonals of a polygon

A line segment connecting non-adjacent vertices of a polygon.

Polygon has n (n-3) diagonals.

2

diagonal

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Sum of Interior Angles of a Polygon

Formula to find Sum of interior angles of a given polygon:

Sum of Interior Angles= 180(n-2), n denotes

the number of sides

Note: Using the above formula, we can find the number of sides and the interior angles of a polygon.

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Each Interior Angle of a Regular Polygon

Let's state the general formula for finding eachinterior angle of a REGULAR polygon

FORMULA: 

Each interior angle of a regular polygon = 180(n-2) ,

where n represents number of sides. n

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Exterior Angles of a Polygon

An exterior angle of a polygon is formed by extending one side of the polygon. The sum of the exterior angles is ALWAYS equal to 360º.

Formula:  Each exterior angle (regular polygon) = 360 ,

where n represents number of sides. n

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Examples

1)What is the name of the polygon with sides 9. Nonagon

2)How many diagonals in a decagon? 20

3)Write the example of convex polygon. Regular pentagon

4) How do you find the number of sides from the formula sum of interior angles = 180(n-2) ? Solve for n

5)Find the sum of the exterior angles of nonagon? 360

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Your Turn

1. Name the polygon : Hexagon

2. Write the number of sides of a polygon: Octagon -

8

3. Draw the diagram of the given polygon: Pentagon

4. Write polygon or not a polygon. Circle Not a

polygon

5. Write the types of polygon. Concave, Convex,

Regular and Irregular

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Your Turn

6. The sum of the exterior angles is ALWAYS equal

to _____. 360 degree

7. Find the sum of the exterior angles of a decagon. 360 degree

8. Find the measure of each exterior angle of a regular hexagon. 60 degree

9. Write the formula to find the sum of Interior angles of a polygon. 180(n-2)

10. Write the example of irregular polygon. Quadrilateral

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Refreshment Time

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Lets play a Game

www.miniclip.com/games/monkey-lander/en/

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1) Find the number of degrees in the sum of the interior angles of an Nonagon. Solution:

An Nonagon has 9 sides.  So n = 9. 

Using our formula from above, that gives us  180(9-2)

= 180(7)

= 1260.

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2) Each interior angle of a regular polygon measures 108.  How many sides does the polygon have ? First, set the formula (for each interior angle)

equal to the number of degrees given.

180(n-2) / n = 108

Cross multiply, 108n = 180(n-2)

Multiply 180 by (n-2), 108n = 180n – 360

Subtract 180n on both sides -72n = -360

Divide both sides by -72, n = 5

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3) The measure of each exterior angle of a regular polygon is 45º.How many sides does the polygon have ?

Set the formula equal to 45. 360/ n = 45

Cross multiply and solve for n. 360 = 45 n

n = 8

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Lets review what we have learned in our lesson

Polygons: A polygon is a closed plane figure made up of 3 or more line segments.

Types of Polygons:

Concave, Convex, Regular and Irregular.

Names of Polygon according to the sides are Triangles, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon and Decagon.

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Formulae

Sum of Interior Angles= 180(n-2), n denotes

the number of sides

Each interior angle of a regular polygon = 180(n-2) where n represents number of sides. n

Each exterior angle (regular polygon) = 360 , where n represents number of sides. n

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You did great in your lesson today !

Do Practice the lesson surely