When constructing a regular hexagon inscribed in a circle, what is the measure of an angle formed by any two adjacent vertices of the hexagon and the center of the circle?

Measure of angle is 60°     

Step-by-step explanation:

Given when constructing a regular hexagon inscribed in a circle, we have to measure an angle formed by any two adjacent vertices of the hexagon and the center of the circle.

we have to find the measure of central angle of hexagon

Total measure of angle at centre is 360°

As polygon is given regular hexagon therefore central angle divides into six equal angles.

Hence, measure of an angle formed by any two adjacent vertices of the hexagon and the center of the circle is

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

75%

step-by-step explanation: