Answer: 27.69⁰
Step-by-step explanation:
Formula for finding the internal angle of a regular polygon is
( 2n - 4 )right angle triangle or
( 2n - 4 )90°, it can also be broken down by factorizing the expression since 2 is common,
( n - 2 )180 or supplementary
Now to find the value of n which correspond to the number of sides the polygon has, we equate the formula to the angle sum of the polygon.
( n - 2 ) × 180° = 1980°
open the bracket
180n° - 360° = 1980°
180n° = 1980° + 360°
= 2340
To find n, divide by 180 which is the coefficient of n
n = ²³⁴⁰/₁₈₀
= 13
The polygon has 13, sides
To find the measure of each angle,
Recall, the sum total of external angle = 360⁰
Therefore, to find the value of each of the angles, we divide 360 by n which is 13
³⁶⁰/n
= ³⁶⁰/₁₃
= 27.69⁰
Answer:
Sides: 13 sides
Measure of each angle: 152.3
Step-by-step explanation:
Since we know the sum of the measures of the interior angles of a convex polygon to be 1,980, we can use the angle-sum theorem formula:
(n-2)180=?
to get our answer.
Equation:
(13-2)180 = 1,980
From here we continue using the angle sum theorem but instead with the intent of finding the measure of each individual interior angle (They will all be equal to the same degree)
Use formula
(n-2)180
n
Equation:
(13-2)180
13
This will give you the answer 152.3.
Sorry if this doesn't explain everything correctly or enough, but I hope I helped. :D
(Btw, if you want more of an explanation as how to properly use formulas to get the number of sides, you can go and check out the answer before mine! It really helps, this answer was mainly to just explain the second answer the way I did it that gave me the correct answer!)
