Have you ever had to get something approved?

Marc and Isaac finished their drawing on time and presented it to the city council. The city council loved their ideas, but did not agree to rebuild the skateboard park in the park. Marc and Isaac were feeling very defeated when they left the meeting.

When they got back to Isaac’s house, there was a message from Principal Fuller at their school. It seems the school has decided to move the soccer field to a bigger space across the street and the boys can submit the design for the new skateboard park right at the school.

“This is great!” Marc says when he hears the news. “Now we can ride before and after school.”

“Yes, but we have to redo our design,” Isaac says. “Let’s get to work.”

The space of the soccer field has been designated by the white lines on the map. To complete their design, the boys will need to count all of the different angles on the map. This way they can figure out where the ramps are going to go and where the rails will also go.

**Do you know how to figure out which angles are which? How many right angles can you count? How many 180 degree angles?** Use the information in this Concept to answer these questions.

### Guidance

Previously we learned to identify different geometric figures and one of them was the ** angle**. Remember that

**an angle is formed when two rays connect at a single endpoint**. You can measure an angle in degrees. When measuring an angle, you are measuring the space between the two rays.

The arc represents the space of the angle that you are measuring. This angle is very small as you can see by the size of the arc.

This arc is very large. The space between the rays is large so the angle is large too.

**We can classify or organize angles according to the size of the angle. Because we measure them in degrees, the angle is classified according to the number of degrees that it has.**

**What types of angles are there?**

1. **Right Angle–the first type of angle is a right angle. It is an angle that is easy to recognize because it forms a corner that is straight. Often with a right angle you will see a little box in the corner too.**

**The corner of this building forms a right angle. You can see buildings like this all the time in the real world. It is an example of a right angle.**

2. **Acute Angle-an acute angle is an angle that is less than 90 degrees. Here is a picture of an acute angle.**

**Here is a picture of an acute angle. You can see that it has been labeled** \begin{align*}45^\circ\end{align*} **to show that it is less than 90 degrees. An acute angle is smaller than a right angle.**

3. **Straight Angle-a straight angle is the same as a straight line. A straight line is equal to** \begin{align*}180^\circ\end{align*}. **The angle of a straight line stretches from one side of the line to the other side as indicated by the arc in this picture.**

**This bike path shows a very straight line in real life.**

4. **Obtuse angle-an obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. Here is a picture of an obtuse angle.**

**This corner forms an obtuse angle. Even if we made a sharp corner from the rounded one, it would still be greater than 90 degrees, but not a straight line, so it is less than 180 degrees.**

Now it is time to try a few on your own. Identify the following angles as acute, obtuse, right or straight.

#### Example A

**Solution: Acute**

#### Example B

**Solution: Right**

#### Example C

**Solution: Obtuse**

Now it is time to reconsider this map and figure out where the different types of angle are located. Be sure to reread the problem!!

Marc and Isaac finished their drawing on time and presented it to the city council. The city council loved their ideas, but did not agree to rebuild the skateboard park in the park. Marc and Isaac were feeling very defeated when they left the meeting.

When they got back to Isaac’s house, there was a message from Principal Fuller at their school. It seems the school has decided to move the soccer field to a bigger space across the street and the boys can submit the design for the new skateboard park right at the school.

“This is great!” Marc says when he hears the news. “Now we can ride before and after school.”

“Yes, but we have to redo our design,” Isaac says. “Let’s get to work.”

The space of the soccer field has been designated by the white lines on the map. To complete their design, the boys will need to count all of the different angles on the map. This way they can figure out where the ramps are going to go and where the rails will also go.

**Do you know how to figure out which angles are which? How many right angles can you count? How many 180 degree angles?**

**By drawing arrows on the school map, we can see where all of the right angles are located. There are eight right angles located on the outside border of the plan for the soccer field.**

These are the angles of the skate park.

### Guided Practice

Here is one for you to try on your own. Look at this picture.

Would you describe the panes of the window as acute, right or obtuse?

**Answer**

If you look at the panes, you can see that they form corners. These "corners" are a big hint as to what kind of angles are present. The panes make up right angles. Right angles are 90 degrees.

### Video Review

James Sousa, Introduction to Angles

### Explore More

Directions: Classify each angle as acute, right, obtuse or straight.

1.

2.

3.

4.

5. An angle measuring \begin{align*}88^\circ\end{align*}

6. An angle measuring \begin{align*}90^\circ\end{align*}

7. An angle measuring \begin{align*}180^\circ\end{align*}

8. An angle measuring \begin{align*}105^\circ\end{align*}

9. An angle measuring \begin{align*}118^\circ\end{align*}

10. An angle measuring \begin{align*}5^\circ\end{align*}

11. An angle measuring \begin{align*}17^\circ\end{align*}

12. An angle measuring \begin{align*}135^\circ\end{align*}

13. An angle measuring \begin{align*}75^\circ\end{align*}

14. An angle measuring \begin{align*}5^\circ\end{align*}

15. An angle measuring \begin{align*}15^\circ\end{align*}