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Learn how to use a protractor to find the exact size of any angle.
Have you ever wondered how a skateboarder knows exactly how to pull off a '360' or how an architect makes sure a roof is steep enough for snow to slide off? They are all using the secret language of angles!
An angle is formed when two straight lines, called rays, meet at a single point called the vertex. Think of an angle as a 'slice' of a giant circle. Just like we use inches to measure length, we use degrees () to measure how 'open' an angle is. A full circle is exactly . If you stand in one spot and spin all the way around, you just turned ! A right angle, which looks like the corner of a square, is exactly .
Quick Check
If a full circle is , how many degrees are in half of a circle?
Answer
A protractor is a semi-circle tool used to measure degrees. To use it correctly, follow the 'Golden Rules': First, place the center mark of the protractor exactly on the vertex of the angle. Second, line up the zero line (the flat bottom edge) with one of the rays. Most protractors have two rows of numbers. Always start counting from the that is touching your ray. If the angle opens to the right, use the scale that starts at on the right side!
Let's measure an acute angle (an angle smaller than a right angle). 1. Place the protractor's center hole on the vertex. 2. Line up the bottom ray with the mark on the inner scale. 3. Look where the second ray points. It points exactly at the mark. 4. The measurement is .
Quick Check
Why do protractors have two sets of numbers (an inner and outer scale)?
Answer
So you can measure angles opening from either the left or the right side.
Sometimes, angles are joined together to make a larger angle. We call these adjacent angles. If you know the measure of the pieces, you can find the total! For example, if you have two small angles sitting side-by-side, the total angle is just the sum: . This also works in reverse. If you know the total and one part, you can subtract to find the missing 'puzzle piece' measurement.
Imagine a large angle that measures . It is split into two smaller angles. One of the smaller angles is . What is the size of the other angle? 1. Start with the total: . 2. Subtract the known part: . 3. Calculate the difference: . 4. The missing angle is .
Three angles meet at a single point to form a straight line (). Angle 1 is and Angle 2 is . What is Angle 3? 1. Add the known angles: . 2. Subtract the sum from the total line: . 3. Angle 3 is .
Where should you place the center mark of the protractor when measuring?
If you are measuring an angle and the ray passes through both and on the scales, and the angle is 'acute' (smaller than a square corner), which is the correct measure?
If two angles combine to form a straight line, and one is , the other must be .
Review Tomorrow
Tomorrow morning, look at a clock. Can you estimate the angle between the hour and minute hands? Is it more or less than ?
Practice Activity
Find five different angles in your house (like the corner of a picture frame or the legs of a chair) and use a protractor to measure them to the nearest degree.