Minds On
Alphabet angles
Record your ideas in a notebook or a method of your choice. What angles can you locate in each letter?
After answering, press the ‘Show Possible Answers’ button to reveal the solutions.
Some students say…
- Z has at least 2.
- Y has at least 3.
- A has at least 5.
- M has at least 3.
- L has at least 1.
- O has zero.
- P has at least 3.
- T has at least 2.
Action
Task 1: Measuring angles
An angle is the space that is created when two lines (rays) come together.
We measure angles in degrees (°) and use a protractor to do so.
A protractor is a curved measuring tool with a straight edge along the bottom.
A protractor usually has a double scale.
The outer scale goes from 0° to 180° and reads clockwise for angles that open clockwise.
The inner scale also goes from 0° to 180° and reads counter clockwise for angles that open counter clockwise.
How to measure an angle using a protractor
To measure an angle with a protractor:
- Align the vertex (common point) of the lines with the midpoint of the protractor (where all the degree angles meet).
- Align one ray (arm of the angle) with the zero line of the protractor, similar to measuring from zero with a ruler.
TIP: Choose the scale that begins at zero and read the measurement where the ray (arm of the angle) crosses the number scale. If the rays open to the right, use the inner scale. If the rays open to the left, use the outer scale.
Task 2: Which angle does not belong?
Explore the following four angles in the interactive protractors provided. To rotate the protractor input the number of degrees you would like to rotate the protractor by and use the buttons to select the direction of rotation.
There is a 180° angle, a 120° angle, a 90° angle, and a 150° angle.
Choose one angle that you think does not belong with the rest and explain why.
To rotate the protractor input the number of degrees you would like to rotate the protractor by and use the buttons to select the direction of rotation.
Which angle does not belong with the rest? Explain your reasoning. After measuring the angles, press the ‘Show Answer’ button to reveal the solutions.
The 180° angle does not belong.
It does not belong because it is not a reflex angle.
The angles were described with their measurements. They can also be categorized into five basic types.
Examine the five types of angles that follow.
An acute angle which is between zero degrees and 89 degrees.
A right angle which measures exactly 90 degrees.
An obtuse angle which is larger than 90 degrees and less than 180 degrees.
A straight angle which measures exactly 180 degrees.
A reflex angle which is more than 180 degrees and less than 360 degrees.
Task 3: Measuring reflex angles
A reflex angle is an angle that is bigger than 180°. Here are some examples: 333°, 233°, and 323°.
A straight line is 180° and a full circle is 360°. How can you use this information to measure a reflex angle?
There are two strategies you can use:
Strategy 1
Measure the inside or the smaller part of the angle then subtract your answer from 360°.
For example, consider an angle that is 27° on its smaller part. What is the reflex angle’s measure?
You have measured 27° on its smaller part. Therefore 360° − 27° = 333°.
The reflex angle measures 333°.
Strategy 2
Extend one of the angle lines to be straight.
Then, measure the angle that goes beyond the straight line.
Next, add that angle and 180°. For example, there is a reflex angle, and a line extending from the angle to form a straight line of 180°.
Following the straight line there is a smaller angle produced which measures 30°.
180° + 30° = 210°.
Task 4: Angle adventure
Conduct some research or use your background knowledge to define each angle and provide a real-world example of that angle.
| Type of angle | Definition (include measurement in degrees) | Real world example |
|---|---|---|
| Acute | ||
| Right | ||
| Obtuse | ||
| Straight | ||
| Reflex |
Complete the Angle Adventure table in your notebook or using the following fillable and printable document. You can also use a method of your choice.
Task 5: Measurement practice
Let’s practice measuring reflex angles with a protractor. Estimate the measure of each angle by inspection or guessing. Then, use a protractor to measure the angles or record a detailed of description of how you would use a protractor to measure each angle. To rotate the protractor input the number of degrees you would like to rotate the protractor by and use the buttons to select the direction of rotation.
To rotate the protractor input the number of degrees you would like to rotate the protractor by and use the buttons to select the direction of rotation.
Task 6: Constructing angles
Making an angle with a specific measurement
Constructing angles is similar to measuring them. Here are the steps:
- Create a straight line.
- Line up the line on the bottom of the protractor on top of the line you created.
- Put the centre of the protractor all of the way to one end of the line.
- Find the measurement that you want and add a dash on the outside of the protractor.
- Using a ruler to connect the dash to the end of the line.
Test Your Skills!
Make six angles with specific measurements
On paper or using digital tools, construct the following angles. Or you may record a detailed description of how you would construct each angle.
- 65°
- 90°
- 133°
- 47°
- 183°
- 317°
Identify the type of angle you created and/or described.
Consolidation
Angle art
Select one of the two options.
Option 1
Create an object using any medium you would like.
You can draw, paint, use digital software, take photographs, or build with items such as string, or popsicle sticks to create a piece that includes all of the types of angles you learned about.
Your piece should have at least 1 type of each of the 5 angles: acute, obtuse, right, straight, and reflex.
You should be able to identify where the angles are located, what type of angle they are, an estimation of the angle, and a measurement of each angle.
Option 2
Use your body to make a series of angles.
Make at least 5 angles, including one of each type: acute, obtuse, right, straight, and reflex.
You should be able to describe how you created these angles, what type of angle it is, an estimation of the angle, and a measurement of each angle.
- What types of angles did you use and why?
- What strategies were needed to complete your work?
Thinking back
Consider the following questions to reflect on your learning. Record your responses using a method of your choice.
- How would you describe how to construct and measure angles to someone?
- What strategies do you use to estimate the measures of angles?
- How might measuring angles be a helpful skill in real life?
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.
Press ‘Discover More’ to extend your skills.
Discover MoreAngles in real life
What occupations use angles? How might angles be important to the following professionals?
- An architect creating a plan for a building.
- A chef cutting equal pieces of a cake. A cake sliced into eight pieces.
Can you think of any other occupations that use angles or protractors?
Record your ideas in a notebook or a method of your choice.
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
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