Question 8.2.1: Angles of an Octagon A stop sign has the shape of a regular ......
Angles of an Octagon
A stop sign has the shape of a regular octagon. A regular octagon is an eight-sided figure with all sides having the same length and all interior angles having the same measure. See Fig. 8.19. Determine
a) the measure of an interior angle.
b) the measure of exterior ∡1.
Step-by-Step
a) Using the formula (n – 2)180°, we can determine the sum of the measures of the interior angles of the regular octagon.
Sum = (8 – 2)180°
= 6 · 180°
= 1080°
The measure of an interior angle of a regular polygon can be determined by dividing the sum of the interior angles by the number of angles. For an octagon,
Measure of one interior angle = \frac{1080°}{8} = 135°
b) Since ∡1 is the supplement of an interior angle,
∡1 = 180° – 135° = 45°
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