Angles and Measuring Angles

Content Angles and Measuring Angles
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Basics on the topicAngles and Measuring Angles

In this measuring angles video…

Nia has found a skateboard in the attic and is learning how to do some cool tricks. As she is practising how to turn the board, she creates different angles. We will help Nia with measuring angles and learn what the tool for measuring angles is called.

Instrument for measuring angles

When we are drawing and measuring angles, we use a special tool called a protractor. When measuring angles with a protractor we need to follow certain steps:

• Measure up the centre of the baseline with the vertex.
• Line up the bottom line with the 0 on the scale.
• Find where the line of the angle intersects with the protractor.
• Read the scale to find the angle measurement.

When you have found the angle you can write it down making sure you use the unit of measure used when measuring angles- degrees. You can use this method when measuring acute angles, measuring right angles and measuring obtuse angles as we will see in the video.

Following the video, have a look at our measuring angles interactive exercises, measuring and drawing angles activities and our measuring angles worksheet.

TranscriptAngles and Measuring Angles

Nia found a skateboard in the attic and is learning how to do some cool tricks! She is practising making turns with the board. We can track her progress by using a special tool called a protractor. "Angles and Measuring Angles." Nia's turns will be measured by the angles they create. Remember, angles are made by two lines that meet at an endpoint, called the vertex. We name the angles by how wide the opening of the arc is and measure these in degrees. Angles can be acute, right, obtuse or straight depending on the opening size. Can you point to the opening, or arc, of each angle? This is the area we need to measure to know what type of angle we have. While we measure Nia’s first turn, let’s take a look at the parts of a protractor. Look at the bottom straight edge. We call this the baseline. It looks familiar, doesn’t it? This ruler is what we will use to make straight lines and it also helps measure the angle openings. In the centre of the baseline, you will see a black dot surrounded by a circle. In order to measure an angle, place this area directly over the vertex and line up the bottom line with the zero on the far left side. Now look at the rounded part of the protractor, called the scale. What do you notice about the numbers on the scale? The scale has two sets of numbers from zero to one hundred and eighty, going in opposite directions. The numbers on the scale go up in tens with smaller dashes that count in fives. To measure, use the set of numbers on the scale that are facing the same direction as your angle opening. Since Nia is facing left we will use the numbers on the outer scale. To determine the degrees of the turn, look at the line that makes up the angle. Which number on the scale does this line intersect with? The line is crossing through the number thirty on the outer scale. Nia moved the skateboard thirty degrees and made an acute angle. Let’s see how far she has moved the board on her next try. First, place the centre of the baseline on the vertex and line up with the zero on the outer scale. Next, you want to see where the top line crosses. What do you notice about where this line intersects? It measures ninety degrees and makes a right angle. Nia has made a quarter turn! On this turn, we can tell that Nia has gone more than ninety degrees, because the opening is wide. Using the protractor, we can find the exact measurement of this obtuse angle. We line up the protractor the same way every time with the bottom line on zero. When we look at the top line, we see that it does not intersect on a number. How can we use what we know about protractors to find this angle? We can find the number that is right before and right after the intersecting line. The numbers are one hundred and thirty and one hundred and forty. Which number is exactly halfway between these two? One hundred and thirty-five! More determined than ever, she gives it another try! When you line up the protractor on this turn, you can see it makes a one hundred and eighty degree angle, which is a straight line! Nia has turned the skateboard in the other direction! Remember, we use a tool called a protractor to measure the size of an angle. We measure by lining up the centre of the baseline with the vertex and the bottom line with the zero on the scale. Then, we count up from zero until we find where the other line intersects with the protractor. Watch out, Nia! Looks like we need to practise going down the ramp!

Angles and Measuring Angles exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Angles and Measuring Angles.
• What's the angle of Nia's turn?

Hints

The horizontal line is aligned with 0. Look to see what number the other line is aligned with.

Look at the numbers on the outermost rim of the protractor.

The angle opens to the left, so look at the numbers that count from left to right.

Solution

The protractor is correctly aligned because the dot is where the two lines meet and the horizontal line is aligned with the 0.

The angle opens to the left, so use the numbers that start counting from the left. These are the numbers on the outer rim of the protractor.

See where the angle's line crosses the protractor. It is halfway between 70 and 80, so the line crosses the protractor at 75.

So, the angle is 75$^\circ$.

• Name the different types of angles.

Hints

An acute angle measures less than 90$^{\circ}$.

An obtuse angle measures greater than 90$^{\circ}$ but less than 180$^{\circ}$.

A right angle measures 90$^{\circ}$.

Solution

To solve this, you can check the exact measurements of each angle. You can also just look to see if they are less than, equal to, or greater than 90$^\circ$.

The first angle is exactly 90$^\circ$, so it is a right angle.

The second angle is greater than 90$^\circ$ and less than 180$^\circ$, so it is an obtuse angle.

The third angle is greater than 90$^\circ$ and less than 180$^\circ$, so it is an obtuse angle.

The fourth angle is less than 90$^\circ$, so it is an acute angle.

The final angle is less than 90$^\circ$, so it is an acute angle.

• Which angles show the given degrees?

Hints

Look to see which way the angle opens to determine whether to use the outer or inner set of numbers.

If the angle opens from the left, start from the 0 on the left and use the outer ring of numbers.

If the angle opens from the right, start from the 0 on the right and use the inner ring of numbers.

Solution

These two angles both measure 125$^\circ$.

• The first one opens to the left. Use the outer ring of numbers to see that the angle aligns with the 125$^\circ$ mark.
• The second one opens to the right. Use the inner ring of numbers to see that the angle aligns with the 125$^\circ$ mark.

• What is the measurement of this angle?

Hints

First, check whether you are using the numbers starting from the left or the right of the protractor.

Find where the angle crosses the protractor to figure out the measurement.

Solution

The angle opens from the right, so read the numbers that start with 0 on the right. These are the smaller numbers on the protractor.

The line crosses the protractor halfway between 140 and 150, which is 145.

So, the angle is 145$^{\circ}$.

• Is the protractor correctly lined up?

Hints

A protractor is correctly aligned when:

• The horizontal line of the angle is aligned with the 0 line on the protractor.
• The dot in the middle of the bottom of the protractor is in the corner of the angle.

Check to see where the protractor's dot aligns with the angle.

Solution

A protractor is correctly aligned when both:

• The horizontal line of the angle is aligned with the 0 line on the protractor.
• The dot in the middle of the bottom of the protractor is in the corner of the angle.

In this problem, the dot was not in corner of the angle. Nia needs to move the protractor so the dot is in the angle's corner, as shown in the image on the right.

• Find the measurement for each angle.

Hints

For each angle, first look to see whether it opens from the right or the left.

Figure out if the angle is acute or obtuse to help you find the correct measurement.

Count in tens and fives to find where the angle crosses the protractor.

Solution

For each angle, first look to see whether it opens to the right or the left.

Then, look to see where the line of the angle aligns with the protractor. Count in tens and fives to find the measurement.