What is the measure of AC?

Step-by-step explanation:

Since no other info is given, you would use a protractor, centered at O. Read off the degree measure, to the nearest degree (a high quality protractor may have divisions to a quarter of a degree). Arc AC has that many degrees.

If the angle is ABC, where B is also on the circle, this is called an inscribed angle, with vertex (its”point”) at B. Now, arc AC will have exactly twice the degree measure of angle ABC. That is a theorem in geometry textbooks, which has been known for about 2500 years!

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