Question

for the regular nonagon below, find the measure of ∠b
select one:
a. 90°
b. 40°
c. 140°
d. 70°
in the image below, what is the order and angle of rotation of the flag?

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular non - agon (9 - sided polygon), let the measure of each exterior angle be \(x\).

Step2: Calculate the measure of exterior angle

Using the formula \(\text{Sum of exterior angles}=n\times x\) (where \(n\) is the number of sides), for \(n = 9\) and sum of exterior angles \(=360^{\circ}\), we have \(x=\frac{360^{\circ}}{n}=\frac{360^{\circ}}{9}=40^{\circ}\). Angle \(B\) is an exterior angle of the regular non - agon, so \(\angle B = 40^{\circ}\).

For the flag (Union Jack of the UK which has rotational symmetry):

Step1: Determine the order of rotation

The order of rotation of a shape is the number of times it can be rotated around a central point and still look the same. The Union Jack flag has an order of rotation of 4.

Step2: Calculate the angle of rotation

The formula for the angle of rotation \(\theta=\frac{360^{\circ}}{\text{Order}}\). Since the order is 4, \(\theta=\frac{360^{\circ}}{4}=90^{\circ}\)

Answer:

1. b. \(40^{\circ}\)
2. Order: 4

Angle: \(90^{\circ}\)