in a regular polygon of N sides the measure of each internal angle is what
a.360°/n
b.n90°
c.2n right angles
d.(2n-4/n)90°
please reply fast
Answers
Answer:
d) .(2n-4/n)90°
Step-by-step explanation:
It is given that ABCDE is n sided polygon.
Take any point O inside the polygon and join OA,OB and OC.
The polygon forms 'n' triangles as it is an 'n' sided polygon.
Since sum of the angles of the triangle is 180 degrees, therefore, sum of the angles of 'n' triangles is =n×180°
which implies
Sum of interior angles + Sum of the angles at O =2n×90° ..........(1)
But the sum of the angles at O is 360 degree ( angles around a point) ..........(2)
Therefore, from equations (1) and (2), we get
Sum of the interior angles + 360 °
=2n×90°
=2n×90° =360 °
=90 °(2n−4)
Thus, sum of the 'n' interior angles =(2n−4)×90
Therefore, each interior angle of a regular polygon =
(2n−4/n)×90 °
hence the answer is option d
In a regular polygon of n sides, the measure of each internal angle is ((2n - 4)/n) 90°
Given :
- A regular polygon of n sides
To Find:
- The measure of each internal angle
Solution:
- A Regular polygon with n sides will have where n ≥ 3
- n Exterior angles
- n Interior angles
- As Polygon is Regular
- All interior angles will be equal
- All exterior angles will Equal
- Sum of Adjacent interior and exterior angle = 180° ( Linear Pair)
- Sum of All the exterior angles of a polygon is 360°
- Right angle measures 90°
Step 1 :
Find Exterior angle
360°/n
Step 2 :
Find Interior angle
180° - 360°/n
= 180°(1 - 2/n)
= 180° (n - 2)/n
= 2 x 90° (n - 2)/n
= 2(n - 2)/n x 90°
= ((2n - 4)/n) 90°
In a regular polygon of n sides, the measure of each internal angle is ((2n - 4)/n) 90°
Correct option is d) ((2n - 4)/n) 90°
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