measure of one external angle of a regular polygon is grater than the measure of one internal angle
a)which is that regular polygon ?
Answers
Answer:
The measurement of one external angle of a regular polygon is greater than the measurement of one internal angle. What type of polygon is this regular polygon?
A triangle. The measure of each exterior angle in a regular polygon is 360°/n, where n is the number of sides.
The measure of the internal angle and its adjacent external angle is always 180°.
In a regular triangle the exterior angles are each 360°/3, or 120°. The interior angles are 180° - 120°, or 60°. This makes the exterior angle greater than the interior angles.
In a regular quadrilateral(square) the exterior angle is 360°/4 or 90°. The interior angles are each 180° - 90°, or 90°. So neither internal nor external angle is bigger than the other.
In any other regular polygon the exterior angles will be less than 90°, so the internal angles will be greater than 90°. So only a regular triangle has larger exterior angles than internal angles.