Section 6.2 Angles of Polygons.

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Presentation transcript:

Section 6.2 Angles of Polygons

Theorems Thm 6.1: Polygon Interior Angles Thm Corollary to Thm 6.1 The sum of the measures of the interior angles of a convex n-gon is (n-2) 180° Corollary to Thm 6.1 The measure of each interior angle of a regular n- gon is (n-2)180 n n for all of these is the number of sides.

Find the measure of each interior angle of a regular pentagon: (5-2)180° 3(180)=540° 540/5= 108°

More Thms cont. Thm 6.2 Polygon Exterior Angles Thm: The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360° Corollary to Thm 6.2: The measure of each exterior angle of a regualr n-gon is (360°)/n

Examples: 1. One exterior angle of a regular convex polygon is 45°. What type of polygon is this? 45= 360/n 45n = 360 n= 8 so octagon 2. One exterior angle of a regular convex polygon is 30 °. What is the sum of the interior angles? 30n = 360 N = 12 (12- 2)180= 1800°

More exs. 3. Each interior angle of a regular convex polygon is 60°. How many sides does it have? 120n= 360 n= 3 4. What is the measure of each interior angle of a regular convex pentagon? 5n = 360 N = 72 180 – 72= 108 5. What is the measure of each interior angle of a regular convex nonagon? 140° 60

More exs. A polygon has 27 sides, all diagonals are drawn from one vertex, how many diagonals are there? 5 sides 3 triangles 2 diagonals 6 sides 4 triangles 3 diagonals 24 N= sides N -2 = # triangles N- 3 = # of diagonals Do it for an octagon N = 8, triangles=6, diagonals= 5