WHO TO MAKE ANGLES BY USING COMPAS

### 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.

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