Interior and Exterior Angles

Slides:

Advertisements

Similar presentations

Objectives Classify polygons based on their sides and angles.

Advertisements

Geometry 5 Level 1. Interior angles in a triangle.

Chapter 24 Polygons.

Objective: To be able to work out the interior and exterior angles of a polygon.

Objectives Classify polygons based on their sides and angles.

Students will name two dimensional figures (9-4).

Problem: What is the degree measure of each interior angle and exterior angle in a regular 18-gon? 18-gon: polygon with 18 sides regular: all angles are.

Polygons A many sided figure.

Do Now 1. What is the value of 5 0 ? a. 5 b. 50 c. 0 d Four stores are having a sale on the same computer. Which store is offering the best sale.

Number of sidesName of polygon 3triangle 4quadrilateral 5pentagon 6hexagon 7heptagon 8octagon 9nonagon 10decagon A polygon is a shape enclosed by straight.

All about Shapes Ask Boffin!.

An Introduction to 2-D Shape Slideshow 15, Mathematics Mr Richard Sasaki, Room 307.

Regular Polygons.  Polygons are a enclosed flat (on the same plane) shape.

8.1.1 Find Angle Measures in Quadrilaterals Chapter 8: Quadrilaterals.

Polygon Basics.

Line Symmetry Slideshow 34, Mathematics Mr Richard Sasaki Room 307.

Shape and Space INTERNAL ANGLES. POLYGON (REGULAR). A polygon is a two dimensional shape with straight sides. There are two types of polygon, regular.

Warm-up Homework out on desks, ready to be checked Prepare a sheet for notes, with the heading: Triangles and Quadrilaterals VOICE LEVEL ZERO.

Exploring Polygons. What are polygons? A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

Polygons By Seaton. Definition A polygon is a shape with at least 3 sides. Poly means many and gon means angles in the Greek language. A polygon is a.

By Mr. Dunfee THE SUM OF THE ANGLES OF A TRIANGLE IS 180 DEGREES.

POLYGONS & QUADRILATERALS

8.2 Angles in Polygons Textbook pg 417. Interior and Exterior Angles interior angles exterior angle.

Geometry. 3 sides 4 sides 5 sides 6 sides 8 sides 9 sides 10 sides 12 sides triangle quadrilateral pentagon hexagon octagon nonagon decagon dodecagon.

The sum of the angles of a triangle is always 180 degrees.

Reviewing angles and polygons

By Mr. Dunfee Be sure to take these notes, or you will not be able to work at the computer.

ANGLES OF POLYGONS. Polygons  Definition: A polygon is a closed plane figure with 3 or more sides. (show examples)  Diagonal  Segment that connects.

Interior angles of polygons This is just one of the six interior angles of this polygon.

Objectives(2): Students will be able to find the sum of measures of the interior angles of a polygon. Students will be able to find the sum of the measures.

8 th Grade Math POLYGONS. A polygon is a plane figure with at least three straight sides and angles, and typically five or more. WHAT IS A POLYGON?

Geometry Name: __________________________ Unit 4 WS 2Date: __________________________ Identify the polygon by name, whether it is convex or non convex,

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.

Geometry In this lesson we revisit all the main rules and terms of line and triangle geometry. We then try and calculate some angles. In the first part,

Polygons Mr Red is going to walk around the outside of the polygon. The black arrow shows the way he is facing as he walks.

Polygons A polygon is a shape made from only straight edges

J.Byrne Types of Triangles pg 1  The sum of the angles in any triangle is 180°  Equilateral Triangle  3 sides and 3 angles are equal  Isosceles.

CLASSIFYING POLYGONS Unit 1 Lesson 6. Classifying Polygons Students will be able to: Identify the 2-dimensional shapes based on their properties. Key.

Polygon Worksheet 1. Concave Polygon Convex Polygon.

Geometry Shapes J.Byrne 2017.

I have five sides and not all of them are the same length.

Shape and Space 2. Polygons

Polygons – Measurements of Angles

Triangle Vocabulary Equilateral:

Polygons 3 triangle 8 octagon 4 quadrilateral 9 nonagon pentagon 10

Y8 Polygon Workbook.

Interior and Exterior angles

Ms. Brittany Uribe Geometry

DO NOT MIX UP THESE OBJECTIVES

Angles in Polygons.

Angle Relationships in Polygons

Classify each quadrilateral below with its best name.

Mr Barton’s Maths Notes

Polygons By Beth Roberts.

ANGLES OF POLYGONS.

Classifying Polygons.

Polygons What? Closed figure; 3 or more line segments that do not cross Name a Polygon Count the number of sides 3 - Triangle 4 - Quadrilateral.

How many diagonals in a… 1. Triangle _______ 2. Heptagon _______

Polygon Name Definition Examples

Math Humor Q: What type of figure is like a lost parrot?

Polygons, Triangles and Quadrilaterals

Mr Barton’s Math Notes 2. Polygons

Names & Properties of 2D Shapes

Mr Barton’s Maths Notes

2D Shape Miss hughes.

1. Who Am I? My total angle measure is 360˚.

Classifying Polygons.

Polygons and Angles Sec 12 -1E pg

Presentation transcript:

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 Pentagon Quadrilateral Hexagon 1260o 900o 1080o 1440o Decagon Septagon / Heptagon Nonagon Octagon 1800o 1620o Hendecagon / Undecagon Dodecagon

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 Triangle What do we call a regular quadrilateral? A square. (A rectangle has two pairs of common lengths but equal angles.)

Calculating angles Example 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. 𝑆𝑢𝑚 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑛𝑔𝑙𝑒𝑠 = 540 𝑜 5 Angle = = 108 𝑜

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). This is a right-angle, it’s 90o. 55o 140o 55 𝑜 + 90 𝑜 + 140 𝑜 +𝑥= 360 𝑜 𝑥 𝑥= 75 0

Answers Easy Triangle – 60o Quadrilateral - 90o Pentagon - 108o Hexagon - 120o Heptagon – 900/7o Octagon - 135o Nonagon – 140o Decagon - 144o Undecagon – 1620/11o Dodecagon - 150o Hard 1. 85o 2. 61o 3. 10o 4. x = 32°; y = 122°; z = 58° 5. x = 70°; y = 55° 6. 86° 2. x=60o

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. An exterior angle is always less than 180o. 72o 108o

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