Angles and Circles

Angles and Circles

Finding angle measurements without a protractor

Let's review

• Angles can be measured in units called degrees ( $\degree$  ).

• When you  find the degrees of an angle, you find its angle measure.

An unit angle is an angle that cuts off $\frac{1}{360}$  of a circle and measures 1 $\degree$  

This straight angle divides a circle into 2 equal parts.

360 $\degree$  $\div$  2  =  180 $\degree$  

So the angle measure of a straight line is 180 $\degree$  

If a circle is divided into four equal parts, you can take 
360 $\degree$   $\div$  4 = to determine the measurement

The angle measure of a right angle is 90 $\degree$  

Multiple Choice

A circular cookie cake is cut into 6 pieces of the same size. What is the angle measure of each piece?

• 360 $\degree$

• 180 $\degree$

• 90 $\degree$

• 60 $\degree$

Remember 1/6 means 1 of 6 equal parts, so divide by 6 to find the angle measure.
360 $\degree$   $\div$  6 = 60 $\degree$  

The angle measure of one section is 60 $\degree$  

Fill in the Blanks

Fill in the Blanks

Multiple Choice

A circle is divided into 9 equal parts. What is the angle measure of one of those parts?

• 9

• 10 $\degree$

• 40 $\degree$

• 360 $\degree$

Fill in the Blanks

Fill in the Blanks

How can we find the measure if two parts are shaded?

First determine the angle measure of one of the parts. So 360 $\degree$   $\div$  5 = 72 $\degree$  

next
2 x 72 $\degree$ - 144 $\degree$  

Multiple Choice

What is the angle measure of  $\frac{3}{8}$ of a circle? 

• 45 $\degree$  

• 90 $\degree$  

• 135 $\degree$  

• 180 $\degree$  

Multiple Choice

 

Mrs. Rodriguez plants roses in  $\frac{4}{9}$  of her circular flower garden. What is the angle measure of the section that includes roses?

• 40 $\degree$  

• 90 $\degree$  

• 160 $\degree$  

• 200 $\degree$  

Determine the measure for one angle.

Multiply the degrees of one angle times the number of parts shaded.

Multiple Choice

How many 30 $\degree$  angles are there in a circle?

• 36

• 12

• 9

• 6