How To Draw A 30 Degree Angle

In this section, we will consider the construction of some angles with special sizes.

Constructing a 60� Angle

We know that the angles in an equilateral triangle are all lx� in size. This suggests that to construct a 60� angle nosotros need to construct an equilateral triangle as described beneath.

Step ane: Describe the arm PQ.
Footstep 2: Identify the bespeak of the compass at P and draw an arc that passes through Q.
Stride 3: Identify the point of the compass at Q and describe an arc that passes through P. Allow this arc cutting the arc drawn in Step two at R.

Constructing a thirty� Bending

Nosotros know that:

So, to construct an angle of 30�, starting time construct a lx� angle and then bisect it. Often, nosotros utilize the post-obit steps.

Step 1: Describe the arm PQ.
Stride 2: Place the bespeak of the compass at P and draw an arc that passes through Q.
Step iii: Place the betoken of the compass at Q and draw an arc that cuts the arc drawn in Footstep 2 at R.
Step 4: With the betoken of the compass still at Q, draw an arc near T every bit shown.
Pace 5: With the point of the compass at R, draw an arc to cut the arc drawn in Pace 4 at T.
Step six: Join T to P. The angle QPT is 30�.

Constructing a 120� Angle

We know that:

This means that 120� is the supplement of threescore�. Therefore, to construct a 120� angle, construct a 60� bending then extend one of its arms equally shown below.

Constructing a xc� Angle

We can construct a 90� bending either by bisecting a straight angle or using the post-obit steps.

Step 1: Draw the arm PA.
Step ii: Identify the point of the compass at P and draw an arc that cuts the arm at Q.
Stride three: 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.
Pace 4: With the indicate of the compass at R, depict an arc of radius PQ to cut the arc fatigued in Step two at S.
Step 5: With the betoken of the compass still at R, draw another arc of radius PQ about T every bit shown.
Step half dozen: With the point of the compass at South, draw an arc of radius PQ to cut the arc fatigued in footstep 5 at T.
Pace 7: Join T to P. The bending APT is 90�.