# GMAT Math : Calculating the angle of a sector

## Example Questions

### Example Question #1 : Calculating The Angle Of A Sector

Note: Figure NOT drawn to scale.

.

Order the degree measures of the arcs  from least to greatest.

Explanation:

, so, by the Multiplication Property of Inequality,

.

The degree measure of an arc is twice that of the inscribed angle that intercepts it, so the above can be rewritten as

.

### Example Question #2 : Calculating The Angle Of A Sector

In the figure shown below, line segment  passes through the center of the circle and has a length of . Points , and  are on the circle. Sector  covers  of the total area of the circle. Answer the following questions regarding this shape.

Find the value of central angle .

Explanation:

Here we need to recall the total degree measure of a circle. A circle always has exactly  degrees.

Knowing this, we need to utilize two other clues to find the degree measure of .

1) Angle  measures  degrees, because it is made up of line segment , which is a straight line.

2) Angle  can be found by using the following equation. Because we are given the fractional value of its area, we can construct a ratio to solve for angle :

So, to find angle , we just need to subtract our other values from :

So, .

### Example Question #3 : Calculating The Angle Of A Sector

The radius of Circle A is equal to the perimeter of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?

Explanation:

Call the length of a side of Square B . Its perimeter is , which is the radius of Circle A.

The area of the circle is ; that of the square is . Therefore, a sector of the circle with area  will be  of the circle, which is a sector of measure

### Example Question #2 : Calculating The Angle Of A Sector

Angle  is . What is angle  ?

Explanation:

This is the kind of question we can't get right if we don't know the trick. In a circle, the size of an angle at the center of the circle, formed by two segments intercepting an arc, is twice the size of the angle formed by two lines intercepting the same arc, provided one of these lines is the diameter of the circle. in other words,  is twice .

Thus,

### Example Question #3 : Calculating The Angle Of A Sector

are  evenly spaced points on the circle. What is angle ?

Explanation:

We can see that the points devide the  of the circle in 5 equal portions.

The final answer is given simply by  which is , this is the angle of a slice of a pizza cut in 5 parts if you will!

### Example Question #4 : Calculating The Angle Of A Sector

The  points  and  are evenly spaced on the circle of center . What is the size of angle ?