Download Exterior Angle Theorem from 4.1 1 A B C

Exterior Angle Theorem from 4.1
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C
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Section 8.1 ~ Angle Measures in Polygons
Topics in this lesson:
• diagonal
• interior/exterior angles
• Polygon Interior Angles Theorem
• Polygon Exterior Angles Theorem
Objective: Use theorems to find interior
and exterior angles of polygons.
Vocabulary
diagonal ­ a segment that joins two nonconsecutive vertices of a polygon
Explore
1) In each polygon, draw all the possible diagonals from one vertex.
2) Complete the table below.
Polygon
# of sides
# of triangles
Sum of interior angles
Triangle
Quad
Pentagon
Hexagon
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n­gon is: *If you have trouble remembering any of the polygon names, refer back to your 1.6 notes and include any that you don't know somewhere in these notes.
Example 1
Find the sum of the measures of the interior angles of a convex octagon.
Example 2
The sum of the measures of the interior angles of a convex polygon is 1260o. Classify the polygon by the number of sides.
Example 3
The sum of the measures of the interior angles of a convex polygon is 1620o. Classify the polygon by the number of sides.
Example 4
Use the diagram. Find the missing angles.
60
40
60
60
115
65
70
65
115
70
Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is 360.
Example 5
Find the value of x.
Example 6
Find the measure of (a) each interior angle and (b) each exterior angle of a regular 15­gon.
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p. 510, #4­20(evens), 11, 21, 22, 26, 30, 32, 39­42