Question 9.2E1: Angles of a Hexagon The surfaces of the heads of many bolts ......
Angles of a Hexagon
The surfaces of the heads of many bolts are in the shape of regular hexagons. A regular hexagon is a six-sided figure with all the sides the same length and all interior angles with the same measure. See Fig. 9.19. Determine
a) the measure of an interior angle.
b) the measure of exterior ∡1.
a) Using the formula (n – 2)180°, we can determine the sum of the measures of the interior angles of a hexagon as follows.
Sum = (6 – 2)180°
= 4(180°)
= 720°
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.
The measure of an interior angle of a regular hexagon is determined as follows:
\text{Measure } = \frac{720°}{6 } = 120°
b) Since ∡1 is the supplement of an interior angle,
m∡1 = 180° – 120° = 60°