In this section, we will consider the construction of some angles with
special sizes.
Constructing a 60º AngleWe know that the angles in an equilateral triangle are all 60º in size. This suggests that to construct a 60º angle we need to construct an equilateral triangle as described below.Step 1: Draw the arm PQ. Step 2: Place the point of the compass at P and draw an arc that passes through Q. Step 3: Place the point of the compass at Q and draw an arc that passes through P. Let this arc cut the arc drawn in Step 2 at R. ![]() ![]() Constructing a 30º AngleWe know that:![]() So, to construct an angle of 30º, first construct a 60º angle and then bisect it. Often, we apply the following steps. Step 1: Draw the arm PQ. Step 2: Place the point of the compass at P and draw an arc that passes through Q. Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R. Step 4: With the point of the compass still at Q, draw an arc near T as shown. Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T. Step 6: Join T to P. The angle QPT is 30º. ![]() Constructing a 120º AngleWe know that:![]() This means that 120º is the supplement of 60º. Therefore, to construct a 120º angle, construct a 60º angle and then extend one of its arms as shown below. ![]() Constructing a 90º AngleWe can construct a 90º angle either by bisecting a straight angle or using the following steps.Step 1: Draw the arm PA. Step 2: Place the point of the compass at P and draw an arc that cuts the arm at Q. Step 3: Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R. Step 4: With the point of the compass at R, draw an arc of radius PQ to cut the arc drawn in Step 2 at S. Step 5: With the point of the compass still at R, draw another arc of radius PQ near T as shown. Step 6: With the point of the compass at S, draw an arc of radius PQ to cut the arc drawn in step 5 at T. Step 7: Join T to P. The angle APT is 90º. ![]() Please print this worksheet to practise the angles construction with the compass: |
Wednesday 23 November 2016
Constructing Angles of 60º, 120º, 30º and 90ºwith the compass
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