Question

A school is designed so that 5 hallways meet at the library in the shape of a regular pentagon. Find the measure of one of the exterior angles of the library.

Answer 1

We do this by dividing 360° by the number of sides, which is 8. (b) Calculate the size of each interior angle in the regular octagon. We do this by subtracting the size of each exterior angle, which is 45°, from 180°. A regular polygon has equal exterior angles of 72°

Answer 2

72°

Explanation:

The external angles of any regular polygon total 360 °.

Now, the formula for calculating an outside angle of the regular polygon is:

360° / n

Where n is the number of sides.

In the case of the regular pentagon it has 5 equal sides and consequently 5 equal exterior angles.

Substituting in the formula, we have

360° / 5 = 72 °

So the exterior angles of the regular pentagon measure 72 ° each.

See attached image.

Hope this helps!