Chapter 14.4, Problem 4PSA

a.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${90}^{\circ }$ .

Calculation:

The angle of ${90}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line  PA .

Step 2:  Put the point of the compass at  P  and draw an arc.

Step 3:  Put the point of the compass at  Q  and with the radius  PQ , cut the arc at R and S.

Step 4:  Now mark point T by placing the point of compass at R and S.

Step 5:  Join  T  to  P . The angle  APT  is 90º.

  

b.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${45}^{\circ }$ .

Calculation:

The angle of ${45}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line segment.

Step 2:  Put the point of the compass at  A  and mark an arc.

Step 3:  Put the point of the compass at the same arc cut the arc at two points.

Step 4:  Now mark a point by placing the point of compass at those two points.

Step 5:  The angle obtained is ${90}^{\circ }$

Step 6: Bisect this angle to obtain the angle of ${45}^{\circ }$

  

c.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${60}^{\circ }$ .

Calculation:

The angle of ${60}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line segment PQ

Step 2:  Put the point of the compass at  P  and mark an arc through Q.

Step 3:  Now, Put the point of the compass at point Q and cut the arc at point R.

Step 4:  Join PR.

Step 5:  The angle obtained is ${60}^{\circ },\angle RPQ={60}^{\circ }$

  

d.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${75}^{\circ }$ .

Calculation:

The angle of ${75}^{\circ }$ can be constructed using the following steps-