In this section, we will consider the construction of some angles with
special sizes.
Constructing a 60º Angle
We 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 Angle
We 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 Angle
We 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 Angle
We 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.
Example 12
Solution:
Activity 10.3
Key Terms
constructing angles
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