Chapter 14.4, Problem 8PSB

a.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${135}^{\circ }$ .

Calculation:

The angle of ${135}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line OA .

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

Step 3:  Now mark point D by placing the point of compass at two points.

Step 4:  Join  O  to  D . The angle  DOA  is 90º.

Step 5: Join E to O. The angle $\angle EOA={135}^{\circ }$

  

b.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is $112{\frac{1}{2}}^{\circ }$ .

Calculation:

The angle of ${90}^{\circ }$ and ${135}^{\circ }$ will be bisected to get the angle of $112{\frac{1}{2}}^{\circ }$ .

c.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${165}^{\circ }$ .

Calculation:

The angle of ${165}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line segment AB.

Step 2:  Draw the angle of ${180}^{\circ }$Step 3:  Now, draw the angle of ${150}^{\circ }$Step 4:  bisect the above two angles to get the angle of ${165}^{\circ }$