Angles and Circles

Angles

What is an angle?

When two lines meet (or intersect) at a point (vertex), then an angle is formed.

Cosmotology

Different Types of Angles

• Acute angles are less than  $90^{\circ}$  

• Right angles are equal to  $90^{\circ}$  

• Obtuse angles are greater than  $90^{\circ}$  

A straight line makes  $180^{\circ}$  

This is called a "straight angle"

This is a  $270^{\circ}$ angle.

A complete circle makes a  $360^{\circ}$ angle.

Multiple Choice

What kind of angle is this?

• A wide one

• Obtuse

• Right angle

• Acute

Multiple Choice

What type of angle is this?

• Acute

• A small one

• Obtuse

• Right Angle

Multiple Choice

How many degrees are in a "straight angle" (a straight line)?

• $90^{\circ}$

• $270^{\circ}$

• $180^{\circ}$

• $360^{\circ}$

Complementary Angles add up to  $90^{\circ}$ 

 $60^{\circ}+30^{\circ}=90^{\circ}$  

These are complementary angles

 $27^{\circ}+63^{\circ}=90^{\circ}$  

Multiple Choice

These angles are complementary, solve for x.

• $1.32$

• $32^{\degree}$

• $0.755$

• $22^{\degree}$

Supplementary angles add up to  $180^{\degree}$  

 $120^{\degree}+60^{\degree}=180^{\degree}$  

These are supplementary angles.

 $146^{\degree}+34^{\degree}=180^{\degree}$  

Multiple Choice

These are supplementar angles, solve for x.

• $55^{\degree}$

• $145^{\degree}$

• $125^{\degree}$

• $215^{\degree}$

Vertical Angles

Vertical angles are angles that are opposite of each other.

Here are examples of vertical angles.

•  $40^{\degree}\approx40^{\degree}$  

•  $140^{\degree}\approx140^{\degree}$  

• Notice the supplementary angles also. 

•  $140^{\degree}+40^{\degree}=180^{\degree}$  

Multiple Choice

Solve for x

• $78^{\degree}$

• $12^{\degree}$

• $102^{\degree}$

Multiple Choice

Solve for a.

• $78^{\degree}$

• $12^{\degree}$

• $102^{\degree}$

• $168^{\degree}$

How do we measure angles?

We use protractors to measure angles.

Can you measure the angle?

Circles

Parts of a Circle

• Center

• Diameter: a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

• Radius: a straight line from the center to the circumference of a circle or sphere.

• Circumference: the enclosing boundary of a curved geometric figure, especially a circle

Pi

•  $\pi=\frac{Circumference}{Diameter}$  

•  $\pi$  is irrational, which means it never ends.

•  $\pi=3.14$ 

Finding Circumference

 $Circumference=d\pi$  
or
 $Circumference=2\pi r$