Question

To Construct Angles of 60°, 30°, 120°, 90°, 45°, 135° and 150° photo
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Answer 1

Answer:

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Step-by-step explanation:

45 Degree Angle

45 Degree AngleConstruct a perpendicular line.

45 Degree AngleConstruct a perpendicular line.Place compass on intersection point.

45 Degree AngleConstruct a perpendicular line.Place compass on intersection point.Adjust compass width to reach start point.

45 Degree AngleConstruct a perpendicular line.Place compass on intersection point.Adjust compass width to reach start point.Draw an arc that intersects perpendicular line.

45 Degree AngleConstruct a perpendicular line.Place compass on intersection point.Adjust compass width to reach start point.Draw an arc that intersects perpendicular line.Place ruler on start point and where arc intersects perpendicular line.

Draw 45 Degree Line.

Constructing a 60° angle

Constructing a 60° angleopen the compass to the same dimensions as our original line.

Constructing a 60° angleopen the compass to the same dimensions as our original line.place the point of the compass on one end of the line and draw an arc.

Constructing a 60° angleopen the compass to the same dimensions as our original line.place the point of the compass on one end of the line and draw an arc.repeat this at the other end and the arcs should intersect where the tip of the triangle should be.

Answer 2

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