Measuring Angles. Lesson Notes. Drawing Angles - Part one. Here are some features of a protractor that you will need to know:

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1 Measuring ngles Drawing ngles - Part one Throughout this lesson, you are going to be using a: Pencil (and occasionally an eraser!) Ruler Protractor Here are some features of a protractor that you will need to know: rigin aseline To draw an angle, start with the vertex. Simply draw a dot somewhere on your page. Label the vertex so that we can refer to it later; choose any letter of the alphabet. We will be using a 180 protractor, but you might have a 360 protractor and that s K too. VERTEX Use your ruler to draw a straight line, starting from the vertex. This straight line is one of the sides of your angle - called a ray. VERTEX RY 1

2 Measuring ngles Rotate your ruler and draw the other side of your angle. VERTEX RY RY nd voila! May I present to you,! may also be named with the use of letters on its rays. Here we could say or, just as long as the letter of the vertex is in the middle. nd finally, arrowheads can be added to the ends of the rays to show that these lines may be extended indefinitely without changing anything about the angle. Now take your protractor and place its origin right over your vertex with its baseline lying along your line; this part is important. Look for 90 at the top of the protractor and place a small mark there. Finally, place your ruler in line with the vertex and the 90 mark and draw a straight vertical line. Right ngles Next is a very special angle. Draw yourself a new vertex, but call it something different from the last one. Use your ruler to draw a horizontal line, starting from the vertex. 2

3 Measuring ngles cute ngles ny angle that is smaller than 90 is called an UTE NGLE; acute meaning sharp. This angle is called a RIGHT NGLE, and we use a little square in the corner to show that it measures 90. Take a few minutes to look around your room. How many right angles you can find? ngles smaller than 90 are called UTE NGLES btuse ngles nd angles larger than 90 are called TUSE NGLES; obtuse meaning dull or blunt. Right angles are used everywhere in construction to build strong and sturdy structures. an you find the right angle amongst this collection of angles? Here it is! ngles larger than 90 but less than 180 are called TUSE NGLES 3

4 Measuring ngles Right, cute and btuse ngles an you tell, just by looking at these angles, which ones are acute and which ones are obtuse? Greater than 90 TUSE NGLE Smaller than 90 UTE NGLE There are two scales on the protractor; one along the outside edge that starts from the 0 mark on the left, and one on the inside that starts from the 0 mark on the right. This is so we can measure angles that open towards the left or towards the right. However, notice that the only scale that has unit markings is the one along the outside edge. For angles that open towards the left, we start from 0 on the outside scale and follow it around until we get to the angle s ray. 128 o Smaller than 90 UTE NGLE Greater than 90 TUSE NGLE Smaller than 90 UTE NGLE Greater than 90 TUSE NGLE L PENS TWRDS THE LEFT This angle measures 128 (more than 90 ) and is therefore an obtuse angle. Measuring ngles Protractors are used to measure angles. ngles are measured in degrees. For angles that open towards the right, we start from 0 on the inside scale. This gets us the tens. Then we have to switch over to the outside scale to get the units. +2 o 30 o 32 o R PENS TWRDS THE RIGHT This angle measures 32 (less than 90 ) and is therefore an acute angle. 4

5 Measuring ngles nytime an angle is in an unusual position, you will need to move your protractor to suit. The important thing is that the origin is right over the vertex and the baseline lies along one of the rays. Now place your ruler in line with vertex and your 45 mark and draw a straight line. +7 o 47 o 40 o 45 o Drawing ngles - Part Two Let s practice maneuvering the protractor. omplete by constructing a 45 angle at vertex. First, place the origin of the protractor on vertex and line up the protractor s baseline along the ray. Notice that the ray meets 0 on the outside scale. Follow the outside scale around to 45 and mark this spot. Measuring ngles The skateboard ramp in the photo was designed by Keith s dad. Determine what angle he used to establish the steepness of the ramp. Since the rays are not long enough to see over the edge of the protractor, we will need to extend them. 5

6 Measuring ngles 2. Determine if is a right angle. +8 o 10 o The skateboard ramp is inclined at an angle of 18. This angle measures 90 and therefore is a RIGHT NGLE. Example 1. Without the use of a protractor, use estimation to label the following angles using the terms: acute, right and obtuse. 3. Measure the acute. Greater than a right angle TUSE NGLE Place the origin of the protractor over the vertex and line up the baseline with one of the rays. Smaller than a right angle UTE NGLE Equal to 90 RIGHT NGLE 6

7 Measuring ngles We will need to extend the rays so that we can see them over the edge of the protractor. Then use the outside scale to find the units. +4 o 77 o 120 o 124 o Follow the outside scale around to the ray and look very carefully for the measure of. = 77 = 124 which makes it an obtuse angle. 5. Determine the portion size of cheese that Marie cut for herself by measuring the central angle of the small section of cheese. 4. Measure and classify it using one of the terms: acute, right or obtuse. Trace over the angle to be measured. Place the origin of the protractor over the vertex and line up the baseline with one of the rays. Notice that the ray meets 0 on the inside scale. Follow the inside scale around to get the tens value of the angle. 7

8 Measuring ngles Line up the baseline of the protractor along a ray, ensuring that the origin is placed over the vertex. Now use the outside scale to find the units. 20 o +7 o Follow the inside scale around to get the tens value of the angle. The small portion of cheese has a central angle of 27. 8