Question

Please help find the measurement of exterior angle MBI

Answer 1

Answer:

The measure of an exterior angle is found by the following formula: Aˆ0B=^AB-^CD2. An interior angle has its vertex at the intersection of two lines that intersect inside a circle. The sides of the angle lie on the intersecting lines. You can find a measure of an exterior angle of a regular polygon with  

N  sides.  It is equal to   360 o N .

Step-by-step explanation:  

Angles of a general polygon (exterior and interior) with more than 3 sides are not defined by the lengths of its sides.  

However, we can calculate the sum of all interior or exterior angles of any convex polygon. It equals to  360 o .

It can be proven geometrically since each exterior angle describes a rotation by some angle and a sum of all exterior angles describes a rotation by full angle of  

360 o . So, if all exterior angles are equal, like in a regular polygon, each one equals to  360 o N .

It can also be defined with some algebraic calculations based on the fact that a sum of all interior angles is  ( N − 2 ) ⋅ 180 o .  

Dividing the above by  N

we will obtain a value of an interior angle:  ( N − 2 ) ⋅ 180o N .  

Therefore, exterior angle of a regular polygon is  180 o − ( N − 2 ) ⋅ 180 o N = 360 o N