Question

prove that the exterior angle of the regular decagon is (360/10) =36°. Interior angle of a regular polygon is 180°-360/5 =108°​

Answer 1

Answer:

the exterior angle of a decagon is equal to 360/10 = 36 degrees. the internal angle of a pentagon is equal to 180 - 360/5 which is equal to 180 - 72 degrees which is equal to 108 degrees. 3 * 36 is equal to 108 degrees. ... for the pentagon, the first formula will become 3 * 180 / 5 = 3 * 36 = 108

Step-by-step explanation:

I hope it helps you

Answer 2

Answer:

tep-by-step explanation:

decagon has 10 sides and sum of the exterior angles of decagon = 3600

∵Decagon is regular

Measuer of each exterior angle = 36010=360−−−−−−−(i)

A pentagon has five sides and sum of interior angles of a pentagon

= (5−2)×1800=3×1800=5400

As pentagon is regular so measure of each angle of the pentagon

=54005=1080−−−−−(ii)

From (i) and (ii)

\frac{measure \: of \: each \: exterior \: angle \: of \: a \: decagon}{measure \: of \: each \: interior \: angle \: of \: a \: pentagon}

measureofeachinteriorangleofapentagon

measureofeachexteriorangleofadecagon

= \frac{36}{108} = \frac{1}{3}=

108

36

=

3/1