Chapter 14, Problem 23RP

a.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is ${30}^{\circ }$ .

Calculation:

The angle of ${30}^{\circ }$ can be constructed using the following steps-

Step 1:  Draw the line PQ .

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

Step 3:  Now mark point R by placing the point of compass at point Q.

Step 4:  Bisect the angle RPQ to get the point T.

Step 5: Join P to T. The angle $\angle TPQ={30}^{\circ }$

  

b.

To determine

To construct the given angle.

Explanation of Solution

Given:

The given angle is $18{\frac{3}{4}}^{\circ }$ .

Calculation:

Bisect the angle ${90}^{\circ }$ and ${120}^{\circ }$ to get the angle of and now bisect the angle to get the angle of ${75}^{\circ }$ and now finally bisect the angle ${37.5}^{\circ }$ to get the angle of $18{\frac{3}{4}}^{\circ }$