Q14. - Geometry

Question

On your paper, draw two angles roughly like those shown. Then for Exercise $11-14$ construct an angle having the indicated measure.  $180-2y$

Step-by-Step Solution

Answer

The figure is,

Step 1. Given information.

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

Angles $x$and $y$ can be constructed as,

Step 2. Concept.

To construct $180-2y$, consider the following ways-

Draw a line $CE$.

Mark the point $B$on line $CE$.

Draw angle $y$ from point $B$.

Place the compass vertex on the angle’s vertex $B$. and mark that point as $s$.

With centre $s$, draw an arc and mark that point as $H$ on the angle $y$.

With centre $H$and without changing the radius of the compass, 

draw another arc and mark that point as $G$.

Draw a line from $B$to where the arcs intersect.

 Mark as $AB$ and $BD$.

Step 3. Apply angle sum property.

According to the angle sum property, 

$\angle ABE=2y$ and $\angle ABC=180-2y$

Step 4. Construct the figure.

The figure is,

Therefore, the required construction is $\angle ABC=180-2y$ as shown above.