43.
Since
n
5
5, the sum of the measures of the
interior angles is 180(5
2
2) or 540. A regular
pentagon has 5 congruent interior angles. Let the
measure of one of these angles be
x
.
540
5
5
x
108
5
x
The measure of each interior angle of the
Pentagon is 108. Since each interior angle and its
corresponding exterior angle form a linear pair,
the measure of the exterior angle is 180
2
108
or 72.
44.
Yes; both the dome and the architectural elements
are based upon a regular octagon.
Since
n
5
8, the sum of the measures of the
interior angles is 180(8
2
2) or 1080. A regular
octagon has 8 congruent interior angles. Let the
measure of one of these angles be
x.
1080
5
8
x
135
5
x
The measure of each interior angle is 135. Since
each interior angle and its corresponding exterior
angle form a linear pair, the measure of the
exterior angle is about 180
2
135 or 45.
45.
}
180(
n
n
2
2)
} 5
}
180
n
n
2
360
}
5
}
180
n
n
} 2 }
3
n
60
}
5
180
2
}
3
n
60
}
The two formulas are equivalent.
46.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles, Regular polygon, interior angles, cosines, Interior Angle

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