1. 10-2: Diagonals and Angle Measure

2. 10-2: Diagonals and Angle Measure
Theorem 10-1: If a convex polygon has n sides, then the sum of the measures of its interior angles is (n – 2)180.
180˚
180˚
180˚
180˚
180˚

3. 10-2: Diagonals and Angle Measure
Example
Landscapers often need to know interior angle measures of polygons in order to correctly cut wooden borders for garden beds. The border at the right is a regular hexagon.
Find the sum of measures of its interior angles.
(6 – 2)(180) = 720˚
Find the measure of one interior angle of the hexagon.
720 / 6 = 120˚

4. 10-2: Diagonals and Angle Measure
YOUR TURN
Refer to the figure at the right.
Find the sum of measures of the interior angles.
1080˚
Find the measure of one interior angle
135˚

5. 10-2: Diagonals and Angle Measure
Theorem 10-2: In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360.
Proof
n linear pairs – sum of interior angles
180n – 180(n – 2)
180n – 180n + 360
360

6. 10-2: Diagonals and Angle Measure
Find the measure of one exterior angle of a regular heptagon
Heptagon = 7 sides
360 / 7  51˚
YOUR TURN
Find the measure of one exterior angle of a regular quadrilateral.
90˚

7. 10-2: Diagonals and Angle Measure
Assignment
Worksheet #10-2