The adjacent interior and exterior angles of a polygon are supplementary, as indicated in the drawing. Assume that you know that the measure of each interior angle of a regular polygon is
|
a) Express the measure of each exterior angle as the supplement of the interior angle. b) Simplify the expression in part (a) to show that each exterior angle has a measure of |
.
a)
To find:
The measure of each exterior angle as supplement of the interior angle.
Given:
The following figure shows the given diagram.
The measure of each interior angle of a regular polygon is
Approach:
Calculation:
The measure of each interior angle of a regular polygon is
In the given figure,
b)
To simplify:
The expression in part (a) to show that each exterior angle has a measure of
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