What’s the answer?

Explanation:

PC = 12 is the radius, so 2*12 = 24 is the diameter

Circumference = pi*diameter = pi*24 = 24pi

Let x be the central angle APC.

To find the length of minor arc AC, we use this formula

L = (x/360)*(circumference)

L is the arc length and x is defined as above. Plug in 24pi for the circumference and plug in L = 68pi/15 which is the shortest distance from A to C along the circle. Solve for x

L = (x/360)*(circumference)

68pi/15 = (x/360)*(24pi)

68pi/15 = pi*x/15

68/15 = x/15 ... divide both sides by pi, the pi terms cancel

68 = x multiply both sides by 15, the denominators cancel

x = 68

The central angle APC is 68 degrees. Therefore, minor arc AC is 68 degrees as well.

Now use the inscribed angle theorem. This says that the inscribed angle is half that of the arc it cuts off. This means inscribed angle ABC is half that of minor arc AC.

angle ABC = (1/2)*(minor arc AC)

angle ABC = (1/2)*(68)

angle ABC = 34 degrees

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer