INTERIOR AND EXTERIOR ANGLES

SLIDESHOW 34, MATHEMATICS

MR RICHARD SASAKI, ROOM 307

OBJECTIVES

Recall and learn the sum of interior angles in certain polygons and their names

Understand the meaning of “exterior angle” and how to calculate them

SHAPE NAMES AND INTERIOR ANGLES

Triangle Quadrilateral Pentagon Hexagon

Septagon / Heptagon Octagon Nonagon Decagon

Hendecagon / Undecagon

Dodecagon

180o 360o 540o

720o

900o 1080o 1260o

1440o

1620o1800o

SHAPE NAMES AND INTERIOR ANGLES

A regular shape is a shape that has all edges the same length. All angles are also the same.Some regular shapes have special

names.

What do we call a regular triangle?An Equilateral TriangleWhat do we call a regular quadrilateral?A square.

(A rectangle has two pairs of common lengths but equal angles.)

CALCULATING ANGLES

With the properties of polygons that we have learned so far, we should be able to calculate a number of angles.

All angles will add up to the sum of interior angles. (Of course!)

Example

Calculate each angle within a regular pentagon.

Angle =𝑆𝑢𝑚𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒𝑠

= =

CALCULATING ANGLES

We can also calculate angles in irregular shapes when one is missing (or two that are the same).

Example

Calculate the missing angle in the shape below.The shape has 4 sides so it’s a quadrilateral (360o).

55o

140o

𝑥

This is a right-angle, it’s 90o.

55𝑜+90𝑜+140𝑜+𝑥=360𝑜𝑥=¿750

ANSWERS

EasyTriangle – 60o

Quadrilateral - 90o

Pentagon - 108o

Hexagon - 120o

Heptagon – 900/7o

Octagon - 135o

Nonagon – 140o

Decagon - 144o

Undecagon – 1620/11o

Dodecagon - 150o

2. x=60o

Hard

1. 85o

2. 61o

3. 10o

4. x = 32°; y = 122°; z = 58°

5. x = 70°; y = 55°

6. 86°

EXTERIOR ANGLES

Exterior angles are angles outside of the polygon that connect with a line.

Exterior angles must join with interior angles so that together, they make 1800.

108o72o

An exterior angle is always less than 180o.

EXTERIOR ANGLES

Next, complete the worksheet given and find out (or if you know, show) what the sum of exterior angles are for given polygons.

ANSWERS

Hopefully you found out (or knew) that the sum of exterior angles is always equal to 360o!

USEFUL NOTATION

Recall some useful notation when looking at shapes…

What do the dashes mean?They imply that this pair of lines are the same length. Also, the angles shown must be the same!

This shape is called an ________ triangle.isosceles

USEFUL NOTATION

For the next notation…What do the arrows mean?They imply that this pair of lines are the parallel. They don’t imply the lines are the same length!

This shape is called a _________.parallelogram