Bell Work Find x 2. Find x and y.

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Presentation transcript:

Bell Work Find x 2. Find x and y

Polygons Day 1 – Interior Angles

This is a chart 3 4 5 6 7 8 n 1 2 3 4 5 6 n -2 Polygon # of Sides # of Triangles Sum of the Angle Measures Interior Angle Measures Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon N-gon 3 4 5 6 7 8 n 1 2 3 4 5 6 n -2

Example 1 Ryan’s parents are building him a sandbox to play in. It is the shape of a hexagon as shown. What is the sum of the measures of the interior angles of the hexagon? 𝑆=180(𝑛−2) 𝑆=180(6−2) 𝑆=180 4 =720

Example 2 The sum of the angles inside a polygon is 2340 degrees. Find the number of sides on this polygon.

Example 3 Find the value of x.

Example 4 Find the value of x.

Regular (Defn) Definition: Can you name a regular quadrilateral? A regular triangle?

How do we find interior angles? Polygon # of Sides # of Triangles Sum of the Angle Measures Interior Angle Measures Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon N-gon 3 4 5 6 7 8 n 1 2 3 4 5 6 n-2 180 360 540 720 900 1080 180(n-2)

Example 5 A regular polygon with each interior angle is 140 degrees. How many sides does the polygon have?

HOMEWORK 6.1 Pg 320 #’s 1-3, 7-9, 13-15, 19-20

Bell Work A mall is designed so that 5 walkways meet at a food court that is in the shape of a regular pentagon. Find the sum of the measures of the interior angles of the pentagon. A polygon that has 53 sides has how many degrees in all of their interior angles?

Polygons Day 2 – Exterior Angles

Sum of Exterior Angles An exterior angle is formed when one side at a vertex of a polygon is extended. The sum of ALL the exterior angles is 360°. FOR EVERY POLYGON!!! This is because the angles rotate around to make one revolution. (circle-has 360 degrees)

Example 1 Find the sum of the exterior angles and the measure of each exterior angle of a… 1. quadrilateral 2. 100-gon 3. nonagon

Example 2 𝐸= 360 𝑛 A hexagon has an exterior angle that measures… The formula for each exterior angle is: 𝐸= 360 𝑛

Example 3 A polygon has an exterior angle of 18 degrees. How many sides does the polygon have?

Example 4 Find the interior and exterior angle measure of a dodecagon

Challenge The ratio for an exterior angle to an interior angle is 1:3. How many sides are in the shape.

Homework 6.1 Pg 321 #’s 10, 16, 17, 23-26, 31