Angles and Measuring Angles

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Angles and Measuring Angles
CCSS.MATH.CONTENT.4.MD.C.6

Information about the video Angles and Measuring Angles

Contents

Measuring Angles

In this video, we will learn about measuring angles with a protractor. Nia found a skateboard in the attic and is learning how to do some cool tricks. As she is practicing how to turn the board, we will learn how to use a protractor.

What is a Protractor?

A protractor is a tool for measuring angles. This device for measuring angles helps us with measuring and classifying angles. (image of protractor)

Examples of Measuring Angles Using a Protractor

Additional Practice with 4th Grade Measuring Angles

Following the video, there is continued measuring angles practice with a measuring angles activity and measuring angles with a protractor worksheet. The measuring angles worksheet will give you hands-on practice measuring angles geometry with examples like measuring 45

Transcript Angles and Measuring Angles

Nia found a skateboard in the attic and is learning how to do some cool tricks! She is practicing 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 center 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 eighty, going in opposite directions. The numbers on the scale are grouped by tens with smaller dashes that count by 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 SECOND line that makes up the angle. What 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 center 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 turned her board HALFWAY! 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(...) bottom line is 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 to solve for this measurement? (...) We can find the number that is right BEFORE and right AFTER the intersecting line. The numbers are one hundred thirty and one hundred forty. What number is exactly halfway between these two? One hundred 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 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 center 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 practice going down the ramp!

Angles and Measuring Angles Exercise

Would you like to practice what you’ve just learned? Practice problems for this video Angles and Measuring Angles help you practice and recap your knowledge.
  • 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.

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

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

    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$^{\circ}$.

    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$^\circ$, so it is an obtuse angle.

    The third angle is greater than 90$^\circ$, 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 to the left, start from the 0 on the left and use the outer ring of numbers.

    If the angle opens to 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 measure 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 after 140, so count 5 more. 140, 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 to the right or the left.

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

    Count by 10s 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 by 10s and 5s to find the measurement.