Download 10.5 Exterior Angle Measure

GEOMETRY
10.5 Exterior and Interior Angle
Measurement Interactions
10.5 Sum of the Exterior Angle Measures
of a Polygon
• Objectives
• Write a formula for the sum of the exterior angles of any polygon.
• Calculate the sum of the exterior angles of any polygon, given the
number of sides.
• Write a formula for the measure of each exterior angle of any
regular polygon.
• Calculate the measure of an exterior angle of a regular polygon,
given the number of sides.
• Calculate the number of sides of a regular polygon, given the
measure of each exterior angle.
Problem 1: Is There a Formula?
• Sum of all the Interior Angles of any Polygon
𝑆𝑢𝑚𝐼𝑛𝑡 = (𝑛 − 2)180𝑜
• An exterior angle of a polygon is formed by extending one
of the sides.
• An exterior angle is supplementary with the interior angle.
They form a linear pair.
Problem 1: Is There a Formula?
• Collaborate 1-5 (10 Minutes)
• 𝑆𝑢𝑚𝐼𝑛𝑡 = (𝑛 − 2)180𝑜
3
4
5
540𝑜
720𝑜
900𝑜
6
7
1080𝑜 1260𝑜
- 180𝑜 - 360𝑜 - 540𝑜 - 720𝑜 - 900𝑜
360𝑜
• Together 6-10
360𝑜
360𝑜
360𝑜
360𝑜
15
2700𝑜
- 2340𝑜
360𝑜
Problem 2: Regular Polygons
• Regular polygons have all sides congruent and all angles
congruent.
• Collaborate 1-5 (5 Minutes)
Problem 2: Regular Polygons
• Together 6-9
360𝑜
360𝑜
360𝑜
360𝑜
360𝑜
360𝑜
60𝑜
90𝑜
108𝑜
120𝑜
128.57𝑜
156𝑜
120𝑜
90𝑜
72𝑜
60𝑜
51.43𝑜
24𝑜
𝑆𝑒 = 360𝑜
𝐸=
360
𝑛
𝑆𝑖 = 720𝑜
𝑛 − 2 ∗ 180
𝐼=
𝑛
360
𝐸=
6
𝐼=
𝐸 = 60𝑜
𝐼 = 120𝑜
720
6
𝐸 = 180 − 𝐼
𝐸 = 180 − 120 = 60𝑜
Formative Assessment
• Skills Practice 10.5
• Pg. 759-762 (1-30)
• 𝑆𝑢𝑚𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 = 360𝑜
𝑆𝑢𝑚𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 = 𝑛 − 2 180𝑜
• 𝐼 + 𝐸 = 180𝑜
•𝐸 =
360
𝑛
𝑛=
360
𝐸