the inner angle of a regular polygon is 144 degree ?
a) what is the measure of outer angle at a vertex ?
b) what is the sum of measures of outer angles?
c) how many does it have ?
Answers
The ans. is
a. 36
b. 360
c. 10
The measure of the outer angle is 36 degrees.
Sum of measures of an outer angle is 360 degrees.
GIVEN: The inner angle of a regular polygon is 144 degree
TO FIND: a) what is the measure of outer angle at a vertex?
b) what is the sum of measures of outer angles?
SOLUTION:
As we are given in the question,
The inner angle of the regular polygon is 144 degrees.
As we know,
Since the interior angle is 144 degrees,
Each exterior angle is 180 - 144 = 36 degrees. (using the angle sum property)
Also,
The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180.
Therefore,
If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.
Hence,
The measure of the outer angle is 36 degrees.
Sum of measures of an outer angle is 360 degrees.
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