Question

Geometry question please help! i'm stuck ):

For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at each vertex?
d. What is the measure of each exterior angle?
e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.

Answer 1

sum of measures of angles is 360 for sure and each angle is 360/n

example: for pentagon n=5 hence each angle is 360/5

Answer 2

its simply n*(360-(360/n)) for each exterior angle I hope :D

Answer 3

for example look at a pentagon, each angle is 72, and we have 288 for each exterior angle, its simply n*360 for the sum b+d

Answer 4

@sriramkumar thats for a quadrilateral. not n-gon.

Sum of angles of a regular n-gon is given by -

Sum of angles = (n-2)180 OR (2n-4)90.

b) Each angles measure is given by

\[\frac{ (n-2)180 }{ n }\]

Answer 5

c) Sum of ALL exterior angles is 360; and every exterior angle is equal to each other for n-gon.

Hence d) Each exterior angle = 360/n.

e) \[\frac{ (n-2)180 }{ n } + \frac{ 360 }{ n }\]

Answer 6

(n-2)180 = 180n-360.

using common denominator n,

\[\frac{ 180n-360+360 }{ n } => \frac{ 180n }{ n } => 180.\]

Answer 7

Hence the sum of interior and exterior angles of any regular n-gon is 180.

Reason -



both the angles are next to each other in a LINEAR PAIR. i.e. they are adjacent angles.

and sum of adjacent angles = 180 hence sum of interior + exterior angles = 180.