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If an exterior angle of a regular polygon is 24", then what is the measure of one of its interior angles.

Sagot :

Angle of a polygon

In any polygon, its exterior angles are the angles that form a straight line with its interior angles:

Then, we have that:

exterior angle + interior angle = 180º

We have that in this case the exterior angle is 24º. Then:

exterior angle + interior angle = 180º

↓ since exterior angle = 24º

24º + interior angle = 180º

↓ taking 24º to the right side of the equation

interior angle = 180º - 24º = 154º

interior angle = 154º

The measure of the interior angles of this polygon is 154º.

Answer: one interior angle = 154 Degrees.

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