Question

Take a regular hexagon Fig 3.10.
1. What is the sum of the measures of its exterior angles x, y, z, p, q, r?
2. Is x=y=z=p=q=r? Why?
3. What is the measure of each?
(1) exterior angle
(i) interior angle
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Answer 1

1. By Using the Fact, that the Sum of Exterior Angles of a Polygon is 360°

$\implies x + y + z + p + q + r = \boxed{360 \degree}$

2. In a Regular Polygon, the Exterior Angles are Equal, as,

$x = y = z = p = q = r = 180 \degree - a$

3.

i)

$x + y + z + p + q + r = 360 \degree$

$6x = 360 \degree$

$x = 60 \degree = y = z = p = q = r$

ii)

Interior Angle of a Regular Polygon of n sides

$= 180 \degree(n - 2)$

$\implies 180 \degree(6 - 2) = \boxed{720 \degree}$