Chapter 10.1, Problem 14WE

To determine

To draw: The angles x and y roughly. Also, draw the angle $180-2y$ .

Answer to Problem 14WE

The figure is:

  

Explanation of Solution

Given information:

The angle to draw is $180-2y$ .

Calculation:

Angles $x\text{and}y$

can be constructed as:

  

To construct $180-2y$ , follow the steps given below

Step 1: Draw a line CE. Mark the point B on line CE.

Step 2: Draw angle y from point B.

Step 3: Place the compass vertex on the angle’s vertex B. and mark that point as S.

Step 4: With centre S, draw an arc and mark that point as H on the angle y.

Step 5: With centre H and without changing the radius of the compass, draw another arc and mark that point as G.

Step 6: Draw a line from B to where the arcs intersect. Mark as AB and BD.

According to the angle sum property, $\angle ABE=2y$ and $\angle ABC=180-2y$

The figure is:

  

Hence, the required construction is $\angle ABC=180-2y$ .