Discover Mathematics P4: Term 2, Unit 13, Lessons 9–12
GoalDraw an angle of a given size with a protractor.
New words
mark · a small dot we draw on the paper at the right number of the scalearc · a small curve drawn inside an angle to show which opening we meanvertex · the point where the two arms of the angle meet
Explanation
To draw an angle of a given size, work in five steps. One: draw a ray with a ruler. Its endpoint will be the vertex. Two: put the centre mark of the protractor on the endpoint and the baseline along the ray. Three: find the number you need on the scale that starts at 0° on your ray, and make a small mark at that number. Four: take the protractor away and use the ruler to draw a second ray from the vertex through the mark. Five: draw a small arc between the rays and write the size. Check with an estimate. For example, an angle of 70° should look smaller than a right angle, and one of 120° should look wider than a right angle. If it does not, you used the wrong scale.
1. Draw a ray→2. Centre mark on the endpoint, baseline on the ray→3. Mark the number on the scale→4. Draw the second ray→5. Add the arc and the size
Worked examples
Draw an angle of 70°. Draw the ray, put the protractor on it with the baseline along the ray pointing right, and find 70° on the scale that starts at 0° on the right. Make a mark there, take the protractor away and join the vertex to the mark.
Draw an angle of 120° with the first ray pointing left. Now the 0° we need is on the left end, so we read the scale that starts from the left. Mark 120° on that scale and draw the second ray. The angle looks wider than a right angle, as an obtuse angle should.
The finished drawing. The angle at O between OA and OB measures 70°. We check: it is smaller than a right angle, so acute, which agrees with the number 70°. The arc shows which opening is 70°.
Class activity
Angle drawing. Draw a ray with a ruler and then draw these angles using your protractor: 30°, 90°, 110° and 150°. Write the size inside each arc. Check each one with the corner of a paper: which are smaller than a right angle, and which are larger? Swap with a friend and measure each other’s angles.
Practice
1
You must draw an angle of 50° with the ray pointing right. Which scale do you use, and does the angle look acute or obtuse?
The scale that starts at 0° on the right. 50° is less than 90°, so the angle is acute.
2
Look at the picture. Does this drawing show an angle of 130°?
Yes, the arm crosses the scale from the right at 130°, and the angle is wider than a right angle.
3
Why do we draw the second ray with a ruler after taking the protractor away?
The mark is only a dot. A ruler joins the vertex to the dot with a straight, exact ray.
4
Draw an angle of 90°. How can you check it without the protractor?
Place the corner of a sheet of paper on it. If the arms fit the paper’s edges exactly, the angle is a right angle.
5
Seif wanted to draw 40° but his angle looks obtuse. What did he do wrong?
He read the wrong scale and marked 140°. He should use the scale that starts at 0° on his ray, and then mark 40°.
