Question

using a ruler and a pair of compass contruct angles of the following measures


a) 30
b)45.
(c) 60
(d) 9o​

Answer 1

Step-by-step explanation:

Year 8 Interactive Maths - Second Edition

Constructing Angles of 60º, 120º, 30º and 90º

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.