How to find the angle of a sector

Practice Questions

PSAT Math › How to find the angle of a sector

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1

Sector

Note: Figure NOT drawn to scale.

Refer to the above figure. The ratio of the area of the white sector to that of the gray sector is 5 to 1. Evaluate .

2

Sector

Note: Figure NOT drawn to scale.

In the above circle, the length of arc is , and the length of arc is . Evaluate .

3

Sector

Note: Figure NOT drawn to scale.

The area of the gray sector in the above circle is . The area of the white sector is . Evaluate .

4

What is the angle of a sector of area on a circle having a radius of ?

5

Sector

Note: Figure NOT drawn to scale.

In the above circle, . Give the ratio of the area of the white sector to that of the gray sector.

6

Circle2

In the figure above that includes Circle O, the measure of angle BAC is equal to 35 degrees, the measure of angle FBD is equal to 40 degrees, and the measure of arc AD is twice the measure of arc AB. Which of the following is the measure of angle CEF? The figure is not necessarily drawn to scale, and the red numbers are used to mark the angles, not represent angle measures.

7

The length of an arc, , of a circle is and the radius, , of the circle is . What is the measure in degrees of the central angle, , formed by the arc ?

8

Circle

In the circle above, the length of arc BC is 100 degrees, and the segment AC is a diameter. What is the measure of angle ADB in degrees?

9

What is the angle of a sector that has an arc length of on a circle of diameter ?

10

A pie has a diameter of 12". A piece is cut out, having a surface area of 4.5π. What is the angle of the cut?

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