Question

An exterior angle of a regular polygon cannot have the measure Select one: a. 90 b. 120 c. 50 d. 40 e. 30

Answer 1

Option c 50 cannot be the measure of exterior angle.

Explanation:

SInce sum of the exterior angles of a polygon is 360

therefore only the angle which can evenly divides 360 can be the measure of exterior angle.

since 360÷90 = 4

360 ÷120 =3

360÷40 = 9

360 ÷30 = 12

360÷50 = 7.2

All the values except 50 divides evenly 360

therefore 50 cannot be the measure of exterior angle

Answer 2

Answer: c. 50

Explanation:

1. By definition, when you add the exterior angles of a regular polygon, you obtain 360 degrees and the number of sides of that polygon can be calculated by dividing 360 degrees by the measure of the exterior angle of it.

2. As you know, the number of sides cannot be fractions, therefore, if you make the folllowing division:

360°/50°=36/5

You obtain a fraction.

3. Then, an exterior angle of a regular polygon cannot have the measure is 50°.