A girl in a helmet stands beside a wooden skateboard ramp

Measure and Sketch Angles

Mia built a skateboard ramp. Is it steep enough for a smooth ride? A protractor will tell us!

4th Grade Math

Step 1: Line It Up

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A protractor measures an angle in degree units. Its scale counts from 0 to 180, like this one. Place the center point on the vertex, where the two rays meet. Which bold mark should the first ray line up with?

Line one ray up with the bold 0 mark. Then the scale counts every degree as the angle opens.

Step 2: Read the Scale

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Mia's ramp makes an angle. One ray sits on the bold 0 mark. The other ray crosses the scale at the bold 30 mark. How many degrees is the ramp's angle?

The angle opens from 0 to 30, so it measures 30 degrees. Start at 0 and count up to where the second ray crosses.

Let's Remember

How to Measure an Angle

          Step 1: Put the protractor's center point on the vertex.

          Step 2: Line one ray up with the 0 mark.

          Step 3: Read the number where the other ray crosses.

One more helper: rays that make a square corner are perpendicular. That angle always measures exactly 90 degrees.

Now Sketch One!

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Sketching runs the steps backward. Draw one ray along the 0 mark. To determine where the second ray goes, find your target number. Mia wants a wide 135 degree angle. Which mark gets the second ray?

Draw the second ray through the bold 135 mark. That angle opens wider than a perpendicular 90 degree corner.

Watch Out! Two Scales

A Common Mistake

          A real protractor prints two numbers at every mark,
          like 60 and 120 at the same spot.

          Reading the wrong scale gives a wrong answer!

First analyze the angle with your eyes. Is it narrower than a square corner? Then it must be less than 90. So the correct reading is 60, not 120.

Measure It!

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One ray sits on the bold 0 mark. The other ray crosses at the bold 80 mark. What is the measure?

The angle opens from 0 to 80, so it measures 80 degrees. It is a little narrower than perpendicular.

Word Problem

Rosa sketches an angle for her kite design. She wants it to open wider than a perpendicular corner. Which measure should Rosa pick for her sketch?

Perpendicular rays form exactly 90 degrees. Wider means greater than 90, so 110 degrees works. 110 > 90.

What Goes in the Blank?

Ben's first ray sits on the 40 mark, not on 0. His angle measures 50 degrees. Where does the second ray cross the scale?

40 + 50 = ?

When a ray starts at 40, add the angle: 40 + 50 = 90. The second ray crosses at the 90 mark.

Which Scale Is Right?

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An angle opens from the bold 0 mark to the bold 60 mark. It looks narrower than a square corner. The protractor's other scale prints 120 at that same spot. Which measure is correct?

Use the scale that counts up from 0 on your ray. A narrow angle must be less than 90, so it measures 60 degrees.

No Ray on Zero!

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This angle's rays cross the scale at the bold 20 mark and the bold 80 mark. Neither ray sits on 0. What is the measure?

Subtract the two marks: 80 - 20 = 60. The angle measures 60 degrees.

Challenge!

Mia checks her finished ramp one last time. The angle's rays cross the protractor at the 35 mark and the 160 mark. Determine the measure of the ramp's angle.

160 - 35 = ?

Subtract the marks: 160 - 35 = 125. The ramp's angle measures 125 degrees, wider than perpendicular.

Where could you measure angles in real life? Think about ramps, roofs, open scissors, and clock hands. Which would be wider than 90 degrees?

Great Work!

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angle degree perpendicular determine analyze