Aim 6.4: To explore the exterior angles of a polygon

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Presentation transcript:

Aim 6.4: To explore the exterior angles of a polygon Do Now: 1. Find the missing angles of the isosceles trapezoid provided below: 2. Solve for x: Homework: Packet page 10 500 x 20 22

Aim 6.4: To explore the exterior angles of a polygon Homework Answers: Packet page 9 1. a) x = 2 b) AC = 10 & BD = 10 2. a) x = 20 b) PQ = 24 c) All sides are 24 so the shape is a rhombus 3. Angle BCD = 80 4. x = 6 5. x = 24 Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon What is a Polygon? A Polygon is a closed figure with three or more sides. A regular polygon is a polygon that is both equilateral and equiangular. Aim 6.4: To explore the exterior angles of a polygon

Number of Triangles in a Polygon Number of Triangles in a Polygon = Number of sides - 2 Aim 6.4: To explore the exterior angles of a polygon

Sum of the Interior Angles of a Polygon Formula: Sum = 180 (n – 2) n represents the number of sides *Think of it as the 180o times the number of triangles 1 3 2 Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Examples: Example #1: Determine the sum of the interior angles of an octagon. Example #2: How many sides does a polygon have if the sum of its interior angles is 720°? Aim 6.4: To explore the exterior angles of a polygon

Measure of Each Interior Angle of a Regular Polygon: Formula: Sum = 180 (n – 2) n This formula can ONLY be used if the Polygon is regular Aim 6.4: To explore the exterior angles of a polygon

What is an Exterior Angle? An exterior angle of a polygon is an angle that is formed by extending the sides of a polygon. Aim 6.4: To explore the exterior angles of a polygon

Exterior Angles of a Polygon All polygons have an exterior angle sum of 360o Exterior angle = 360 n n represents the number of sides This formula can ONLY be used if the Polygon is regular Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #1: Find the sum of the interior angles of a hexagon (six sides) equals: Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #2: How many degrees are there in each interior angle of a hexagon? Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #3: How many sides does a polygon have if the sum of its interior angles is 2160° ? Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #4: Each interior angle of a regular polygon measures 162°. How many sides does the polygon have? Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #5: Find the number of degrees in each exterior angle of a regular pentagon: Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Example #6: What is the sum of the exterior angles of a polygon with 36 sides? Aim 6.4: To explore the exterior angles of a polygon

Aim 6.4: To explore the exterior angles of a polygon Exit Ticket: True or False: In a regular polygon, all sides and angles are congruent. The formula for the measure of each interior angle is Exterior angle = 360 n Determine the sum of the interior angles of a 30 sided figure: Aim 6.4: To explore the exterior angles of a polygon