Chapter 14, Problem 1CTE

To determine

To construct: an angle of measure $22{\frac{1}{2}}^{\circ }$ .

Answer to Problem 1CTE

  

Explanation of Solution

Given information:

To construct an angle of angle half of ${45}^{\circ }$ .

Calculation:

We can write ${45}^{\circ }=22{\frac{1}{2}}^{\circ }+22{\frac{1}{2}}^{\circ }$ .

Step-1 Draw a line $AB$ and make a semicircle around $A$ which cut $AB$ at $D$ .

  

Step-2 Draw a perpendicular $AE$ on $A$ which cut the semicircle at $G$ . Now take the length $GD$ and make cut from both point $G$ and $D$ , it will cut at point $H$ . Extend $AH$ to $F$ . We get two equal measured angle $\angle GAF=\angle BAF={45}^{\circ }$ .

  

Step-3 Next to divide $\angle BAF$ into two same angle take the length $LD$ and cut from each point of $L$ and

  $D$ so that it will cut at the point $K$ .

  

Extend the point $A$ and $K$ to $J$ so that it will divide $\angle BAF$

into two equal angle that is now,

  $\begin{array}{l}\angle BAF=\angle LAJ+\angle JAB\\ \Rightarrow {45}^{\circ }=22{\frac{1}{2}}^{\circ }+22{\frac{1}{2}}^{\circ }\end{array}$

Hence $\angle LAJ,\angle JAB$ are such angle of measure $22{\frac{1}{2}}^{\circ }$ .