If you draw a regular polygon whose exterior angles are p,l,a,n,e and each interior angle
is x°, what is the measure of each exterior angle?
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Answer:
The sum of exterior angle and its adjacent interior is 180
0
, that is,
e+i=180
0
Since each interior angle is twice its adjacent exterior angle, therefore, substitute i=2e.
e+2e=180
0
⇒3e=180
0
⇒e=
3
180
0
=60
0
We know that the measure of exterior angle is e=(
n
360
)
0
where n is the number of sides.
Here, it is given that the exterior angle is e=60
0
, therefore,
n=
e
360
=
60
360
=6
Hence, the number of sides is 6.
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