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Answer:
(a)I. 13 Sides II. 7 Sides
(b) 4 Sides, Square
(c)x=52 degrees
(d)x=107 degrees
(e)1620 degrees
Step-by-step explanation:
(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.
I. If the Interior angle is
Then:
The polygon has <u>13 sides.</u>
II. If the Interior angle is
Then:
The polygon has <u>7 sides.</u>
(b)The sum of the exterior angle of a polygon is 360 degrees,
Each exterior angle of a n-sided regular polygon is:
If the exterior angle of a regular polygon is 90°
Then:
The regular polygon has 4 sides and it is called a <u>Square.</u>
<u>(c)</u>The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.
Each Interior angle of a regular n-sided polygon is:
For a pentagon, n=5
Then:
(d)The <u>sum of the exterior angle of a polygon is 360 degrees.</u>
If four of the exterior angles of a pentagon are 57, 74, 56, and 66.
Let the fifth angle=x
Then:
(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.
In an 11-gon., n=11
Therefore, the sum of the interior angle=(11-2)180=
The sum of the interior angle <u>does not change either in a regular or irregular polygon.</u>