Question 1019530
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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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<U>Answer</U>. Leena is right.


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<U>Solution</U>

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 = {{{180/5}}} = 36.

Thus the exterior angle is 36 degrees.
(The interior is 4*36 = 144).

Now, the sum of exterior angles of any polygon is  {{{360}}} degrees.

Hence, the number of vertices is  {{{360/36}}} = 10.
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