SOLUTION: the ratio of exterior angles and the interior angles of a regular polygon is 1:4. leena says the polygon is a regular decagon while linda says it is regular pentagon. who is right
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Question 1019530: the ratio of exterior angles and the interior angles of a regular polygon is 1:4. leena says the polygon is a regular decagon while linda says it is regular pentagon. who is right Answer by ikleyn(52809) (Show Source):
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The ratio of exterior angles and the interior angles of a regular polygon is 1:4.
Leena says the polygon is a regular decagon while Linda says it is regular pentagon. who is right
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Answer. Leena is right.
Solution
Let x be the measure of the exterior angle, in degrees.
Then the measure of the interior angle is 4x, according to the condition.
And the sum of x and 4x is 180 degrees:
x + 4x = 180 ---> 5x = 180 ---> x = = 36.
Thus the exterior angle is 36 degrees.
(The interior is 4*36 = 144).
Now, the sum of exterior angles of any polygon is degrees.
Hence, the number of vertices is = 10.
