find the number of sides of a regular polygon whose each exterior angle is half of its interior angel
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The sum of exterior angle and its adjacent interior is 180
0 , that is, e+i=180 .Since each exterior angle is equal to half its adjacent interior angle, therefore, substitute 2
i
=e or i=2e.
e+2e=180
0
⇒3e=180
⇒e=
3
180
0
=60
We know that the measure of exterior angle is e=( n )
360
where n is the number of sides. Here, it is given that the exterior angle is e=60 , therefore,
n= e
360
= 60 /360
=6
Hence, the number of sides is 6.
Step-by-step explanation:
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