Interior and Exterior Angles of Polygons. To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex.

Slides:

Advertisements

Similar presentations

Interior and Exterior Angles of Polygons

Advertisements

Warm Up A three sided polygon is called a __________.

Geometry 6.1 Prop. & Attributes of Polygons

6.1: Properties of Polygons

Entry task The car at each vertex of a Ferris wheel holds 5 people. The sum of the interior angles of the Ferris wheel is What is the maximum number.

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

Properties and Attributes of Polygons

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

WARM-UP Tuesday, February 24, 2015

6.1: Polygon Angle Theorems

Section 6.2 Angles of Polygons.

Geometry Chapter Polygons. Convex Polygon – a polygon with a line containing a side with a point in the interior of the polygon.

Ch 3.5 Standard 12.0: Students find and use measures of interior and exterior angles of triangles to classify figures and solve problems. Standard 13.0.

(over Lesson 10-1) Slide 1 of 1 1-1a.

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

6-1 Properties and Attributes of Polygons Holt McDougal Geometry

6.1 Classify polygons based on their sides and angles.

Chapter properties of polygons. Objectives  Classify polygons based on their sides and angles.  Find and use the measures of interior and exterior.

ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS. POLYGONS NOT POLYGONS.

8-1 Find Angle Measures in Polygons Warm Up Lesson Presentation

Objectives Classify polygons based on their sides and angles.

1 Tambourines The frame of the tambourine shown is a regular heptagon. What is the measure of each angle of the heptagon? Angles and Polygons 13.3 LESSON.

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

Lesson 8.2 (Part 2) Exterior Angles in Polygons

11-1 Angle Measures in Polygons Warm Up Lesson Presentation

8.2 Angles in Polygons Polygon Number of sides Number of triangles Sum of measures of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon.

Geometry Section 8.1 Find Angle Measures in Polygons.

Warm Up 7.3 Formulas involving Polygons Use important formulas that apply to polygons.

Polygons and Quadrilaterals I can classify polygons and find their angle measures.

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.

Warm Up 1. A ? is a three-sided polygon.

Holt McDougal Geometry 6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Holt Geometry Warm Up Warm Up Lesson Presentation.

Holt Geometry 6-1 Properties and Attributes of Polygons Warm Up 1. A ? is a three-sided polygon. 2. A ? is a four-sided polygon. Evaluate each expression.

Do Now. Section 8.2 Angles in Polygons Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex polygon with n sides.

Lesson 5.2 Polygon Exterior Angle Sum HOMEWORK: 5.2/ 1-10.

Informal Geometry 10.2 Diagonals and Angle Measure.

Properties and Attributes of Polygons Entry task The car at each vertex of a Ferris wheel holds 5 people. The sum of the interior angles of the Ferris.

Day 1 Properties of polygons. A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints.

Holt McDougal Geometry 6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Holt Geometry Warm Up Warm Up Lesson Presentation.

Section 8.2. Find the measures of the interior angles of a polygon. Find the measures of the exterior angles of a polygon.

Polygons 1 What is the difference between concave and convex?

Polygons. Polygon Interior Angle Theorem The sum of the measures of the interior angles of a convex polygon is given by: Sum = 180(n – 2) where n represents.

8.2 ESSENTIAL QUESTION: How do you calculate the measures of interior and exterior angles of polygons?

Objectives Classify polygons based on their sides and angles.

Polygons Subtitle.

8.1 – Find Angle Measures in Polygons

Objectives Classify polygons based on their sides and angles.

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

8.1 Angles of Polygons What you’ll learn:

6-1 Angles of Polygons The student will be able to:

Lesson 8-1 Angles of Polygons Lesson 3-4: Polygons.

Vocabulary side of a polygon vertex of a polygon diagonal

Objectives Vocabulary

Lesson 3.3 Objective/Topic: Determine the sum of interior angles of a polygon. To determine the measures of exterior angles of a polygon. Essential Question:

6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation

Find Angle Measures in Polygons

Angle Relationships in Polygons

8.1 – Find Angle Measures in Polygons

6-1 Properties and Attributes of Polygons Lesson Presentation

6.1 properties and attributes of Polygons

Pearson Unit 1 Topic 6: Polygons and Quadrilaterals 6-1: The Polygon Angle-Sum Theorems Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007.

Two-Dimensional Figures

Objectives Classify polygons based on their sides and angles.

ANGLES OF POLYGONS.

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

Warm Up 9/21 What is the measure of each angle in a regular octagon?

Math 132 Day 4 (2/8/18) CCBC Dundalk.

Day 1 Properties of polygons

Vocabulary side of a polygon vertex of a polygon diagonal

ANGLES OF POLYGONS SECTION 8-1 JIM SMITH JCHS.

Presentation transcript:

Interior and Exterior Angles of Polygons

To find the sum of the interior angle measures of a convex polygon, draw all possible diagonals from one vertex of the polygon. This creates a set of triangles. The sum of the angle measures of all the triangles equals the sum of the angle measures of the polygon.

In each convex polygon, the number of triangles formed is two less than the number of sides n. So the sum of the angle measures of all these triangles is (n — 2)180°.

Example 3A: Finding Interior Angle Measures and Sums in Polygons Find the sum of the interior angle measures of a convex heptagon. (n – 2)180° (7 – 2)180° 900° Polygon  Sum Thm. A heptagon has 7 sides, so substitute 7 for n. Simplify.

Example 3C: Finding Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of pentagon ABCDE. (5 – 2)180° = 540° Polygon  Sum Thm. mA + mB + mC + mD + mE = 540° Polygon  Sum Thm. 35c + 18c + 32c + 32c + 18c = 540Substitute. 135c = 540Combine like terms. c = 4Divide both sides by 135.

Example 4B: Finding Interior Angle Measures and Sums in Polygons Find the value of b in polygon FGHJKL. 15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360° Polygon Ext.  Sum Thm. 120b = 360Combine like terms. b = 3Divide both sides by 120.