Question

In circle C the measure of arc AB=72. Find the measure of angle BCD

Answer 1

108

Explanation:

the answer would be 108. 72+108=180, and the circumference of a circle is 360. the other half equals 180, so 180+180=360.

Sorry if i'm bad at explaining...

Answer 2

When we have a circle of radius R, we have that the total perimeter of the circle is equal to:

P = 2*pi*R

Now, if we have an arc, this is only a section of the total perimeter, the measure of the arc is equal to:

A = (θ/2*pi)*2*pi*R = θ*R

You can see that when θ = 2*pi, the term in the left is equal to 1 and we have the complete perimeter.

Now, we have that the measure of the arc AB = 72, then we can find the angle as:

A = 72 = θ*R

then we solve this for theta:

72/R = θ

Where you can see that as bigger is the radius of the circle, smaller is the value of theta.

Remember that this equation works with angles in radians.