How to find the angle for a percentage of a circle

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ISEE Upper Level Quantitative Reasoning › How to find the angle for a percentage of a circle

Questions 1 - 5

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

$154.8^{\circ}$

$15.5^{\circ}$

$430^{\circ}$

$366^{\circ}$

Explanation

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

Use the following formula and solve for x:

$\frac{x}{360^{\circ}}100=43%$

Begin by dividing over the 100

$\frac{x}{360^{\circ}}=.43$

Then multiply by 360

$x=.43*360^{\circ}=154.8^{\circ}$

Generalsector

What is the angle measure of in the figure above if the sector comprises 37% of the circle?

Explanation

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle. To do this, you merely need to multiply by ˚. This yields ˚.

Generalsector

What is the angle measure of in the figure above if the sector comprises % of the circle?

Explanation

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle. To do this, you merely need to multiply by ˚. This yields ˚.

What is the angle measure of in the figure if the sector comprises of the circle?

Generalsector

Explanation

It is very easy to compute the angle of a sector if we know what it is as a percentage of the total circle. To do this, you merely need to multiply by ˚. This yields ˚

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

$162^{\circ}$