You need to construct a regular polygon. When you draw two sides, the interior angle created between them is 144°, illustrated below.

Question

anonymous · Answer

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anonymous · Answer

What will be the sum, in degrees, of the measures of the interior angles of this polygon when it is completed?

directrix · Answer

Do you know or use the formula for the sum of the angles of a convex polygon with n sides?

shayaan_mustafa · Answer

for regular polygons$$\large \frac {180(n-2)}{n}$$

shayaan_mustafa · Answer

where n= number of sides

directrix · Answer

If the interior angles of a regular polygon is 144, then the adjacent and supplementary exterior angle has measure 36. The sum of the exterior angles of a regular polygon is 360. If each angle has measure 36 and the exterior angles sum to 360, then there are 360/36 = 10 exterior angles and 10 interior angles. The polygon is a decagon with 10 sides.

The sum of the interior angle measures would then be 10(144) = 1440.