7.1 Interior and Exterior Angles in Polygons. What is the sum or the interior angles in a triangle? 30 ° 60 ° 100 ° 30 ° 50 ° 60 ° 80 ° 60 ° 40 ° 80 °

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Presentation transcript:

7.1 Interior and Exterior Angles in Polygons

What is the sum or the interior angles in a triangle? 30 ° 60 ° 100 ° 30 ° 50 ° 60 ° 80 ° 60 ° 40 ° 80 ° 20 ° 45 ° 180 °

What is the sum of the interior angles of these polygons?

Sum of interior angles of convex polygon: S = (n-2)180 Where n is the number of sides and S is the sum of the angles.

Measure of interior angle of a regular n- gon: a = (n-2)180 n

Ex. 1 The figure below is a regular polygon. Find the sum of the interior angles and the measure of one interior angle.

Ex 2. The sum of the interior angles of a polygon is 2700°. How many sides does the polygon have?

Ex 3 – Find the measure of each interior angle of a regular dodecagon.

Ex. 4 – Find x. 130° 110° 120° 160° x

Exterior Angles in a Polygon

Sum of exterior angles in a polygon:

Polygon Exterior Angles Theorem: The sum of the exterior angles of any convex polygon is 360°.

As the number of sides increases, what happens to each exterior angle of a regular polygon? The sum stays the same, so each individual angle becomes smaller.

Ex. 5 – Find the sum of the exterior angles of a heptagon.

Ex. 6 – Find one exterior angle of a regular nonagon.

Ex. 7 – Find x.

Ex. 8 Find the number of sides of a regular polygon if one interior angle is 162°.