# ACT Math : How to find the angle for a percentage of a circle

## Example Questions

### Example Question #1 : Sectors

The sector pictured above is  of the circle. What is the angle measure  for the sector?

Explanation:

A question like this is very easy. You merely need to find out what is  of the total  degrees in a circle. This is:

. That is it!

### Example Question #2 : Sectors

The area of sector  is . This figure is not drawn to scale.

What is the measure of the angle of the sector?

Explanation:

You know that the area of a circle is computed by the equation:

For our data, this is:

or

Now, the sector is a percentage of the circle. For the areas, this can be represented as the fraction:

The total degree measure of a circle is, of course,  degrees.  This means that the sector contains:

.

### Example Question #1 : How To Find The Angle For A Percentage Of A Circle

The arc length of sector above is . This figure is not drawn to scale.

What is the angle measure of sector ?

Explanation:

You know that the circumference of a circle is computed by the equation:

For our data, this is:

Now, the sector is a percentage of the circle. For the lengths of the circumference and the arc length, this can be represented as the fraction:

The total degree measure of a circle is, of course,  degrees. This means that the sector contains:

.

### Example Question #2 : How To Find The Angle For A Percentage Of A Circle

Sector  is  of the total circle. This figure is not drawn to scale.

What is the angle of this sector?

Explanation:

Do not overthink this question! All you need to remember is that a given circle contains  degrees. This means that the sector is merely a percentage of . For our question, this percentage is , which is the same as . So, to calculate, you merely need to multiply:

This is the degree measure of the sector.

### Example Question #3 : How To Find The Angle For A Percentage Of A Circle

A bike wheel has  evenly spaced spokes spreading from its center to its tire. What must the angle be for the spokes in order to guarantee this even spacing? Round to the nearest hundredth.