In a regular dodecagon by how much does the interior angle exceed the exterior angle?

A dodecagon has 12 sides

The way I remember is "decagon = 10 sides" and "do = duo = 2" so 10+2 = 12.

The measure of each exterior angle of a regular polygon is found by this formula

E = 360/n

plug in n = 12 to get

E = 360/n

E = 360/12

E = 30

Each exterior angle of a regular dodecagon is 30 degrees. The interior angle is 180-E = 180-30 = 150 degrees

Interior angle = 150 degrees

Exterior angle = 30 degrees

Subtract the values: 150 - 30 = 120

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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answer: d.) the total number of protons and neutrons is 15

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