8-1: Angles of Polygons. Diagonal-a line that connects any two vertices that are not next to each other. If diagonals are drawn from one vertex it splits.

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Presentation transcript:

8-1: Angles of Polygons

Diagonal-a line that connects any two vertices that are not next to each other. If diagonals are drawn from one vertex it splits the shape into triangles. Sum of interior angles of a Δ = 180 Number of sidesNumber of trianglesSum of < measures 31(1x180)=180 42(2x180)=360 53(3x180)=540 64(4x180)=720 75(5x180)=900

Find the sum of the interior angles of a… gon2. 13-gon gon4. n-gon This is the Interior Angle Sum Thm.

Exterior Angle Sum Theorem: For any polygon: The sum of the measures of the exterior angles equals 360 degrees. m<1+m<2+m<3+m<4+m<5=360

Regular polygon - the lengths of all sides and measures of all angles are equal.

Find the measures of the exterior angles of a … 1.Regular octagon 2.Regular pentagon

Regular polygons To find the measure of each interior angle: –Find the exterior angle by doing 360/n. –Find the interior angle by doing 180-exterior. EX: Find the measure of each interior angle of a regular heptagon.

Finding the number of sides. All polygons are regular. 1. Interior angle=135 Number of sides = ____________ 2. Interior angle = … Number of sides = ____________

Find x and the measure of each interior angle.

Assignment: p. 407; odd, odd CHECK YOUR ANSWERS IN THE BACK OF THE BOOK.