Question

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 ?​

Answer 1

The ans. is

a. 36

b. 360

c. 10

Answer 2

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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