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:

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Presentation transcript:

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: What is the sum of the exterior angles of a polygon? We know the sum of the interior angles of triangles and quadrilaterals. Sum of the angles 180⁰ Sum of the angles is 360⁰

Draw a segment on the figure to create two triangles. The sum of the angles in each triangle is 180⁰. Therefore the sum of the angles of the rectangle is 360⁰.

Draw segments from a single vertex to divide polygon into triangles. There are three triangles each with a sum of 180⁰ 3 ∙ 180 Total sum of angles of pentagon is 540⁰

≈128.57 Divide 900 by 7 to determine each angle. Determine the sum of the interior angles of the regular figure. 7 Sides (n – 2) ∙ 180 (7 – 2) ∙ 180 5 ∙ 180 900⁰ Divide 900 by 7 to determine each angle. ≈128.57

Exterior Angles:

Find the measure of the exterior angle.

Z = 105 124 + z + 26 + z = 360 2z = 210 Determine the value of z

1080 ÷ 8 Practice Each angle is 135⁰ (n – 2) ∙ 180 (8 – 2) ∙ 180 Determine the sum of interior angles in a regular Octagon. (n – 2) ∙ 180 (8 – 2) ∙ 180 6 ∙ 180 1080 Then determine the measure of each of the angles. 1080 ÷ 8 Each angle is 135⁰