Question

measure of one external angle of a regular polygon is grater than the measure of one internal angle ​

Answer 1

Answer:

8th

Maths

Understanding Quadrilaterals

Angle Sum Property

Let the formula relation th...

MATHS

Let the formula relation the exterior angle and number of sides of a polygon be given as nA=360.

The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50, what is the greatest number of sides it can have?

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ANSWER

Sum of exterior angles for any polynomial is always 360.

Since polynomial has n angles, each with exterior angle is A, then

sum of exterior angles will be nA

Given, nA=360

∴A=

n

360

We are given that: A>50

⇒

n

360

>50

⇒360>50n

⇒n<

50

360

⇒n<7.2

Hence, the greatest number of angles polygon can have is 7.

Answer 2

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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.