Respuesta :

One way is to first find the measure of one external angle:-

Measure 1 ext angle = 360 / 10 = 36 degrees (Note the sum of the external angles of all polygons is 360  degrees)

So the internal angle = 180 - 36 = 144

So sum of the internal angles

= 10 * 144

= 1440  degrees (answer)

decagon

All sides are the same length (congruent) and all interior angles are the same size (congruent).


To find the measure of the angles, we know that the sum of all the angles is 1440 degrees (from above)...  And there are ten angles...


decagons


So, the measure of the angle of a regular decagon is 144 degrees.sum of exterior angles always=360°


for n-sided polygon,


sumo of exterior angles+sum of interior angles =180×n°


sum of interior angles=180n° -360°=180n°-180°×2=180(n-2)°


For decagon, n=10,


sum of its interior angles =180×10°–360°=1800°–360°= 1440°



so your answer is 1440°

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