Construction of Angles

Construct an angle of $22.5°$ using ruler and compass.

Construct an angle which is half of $30°$ using ruler and compass.

Construct an angle which is one-third of $45°$ using ruler and compass.

Construct an angle of $15°$ using ruler and compass.

Steps of construction:

2. With point $P$ as centre and the same radius, mark an arc and name it as $F$. Again put your compass at $F$ and with the same radius, draw an arc which intersects the initial arc at $E$.

3. Fix your compass at $E$, draw an arc with a convenient radius. Repeat the process by putting the compasses at $F$ and let the two arcs intersect at $B$. Join $OB$. $\angle BOA=90°$.

4. Now, bisect the obtained angle between $BO$ and $OA$. Mark it as $OC$. $\angle COA=$ _____$°$

It is possible to construct the angle $135°$ using a compass and ruler.

In the first square paper, the sides $AB, AD$ are folded about the corner point $A$, in a way as shown in figure $2$, so that the two folded parts overlaps each other perfectly.

When it is unfolded, the folds are marked as in figure $3$.

It is found that, $\angle DAE=\angle EAF=\angle FAB=30°$

$\angle BAE=\angle DAF=60°$

Again if the side $AD$ is folded about the point $A$ such that $AD$ coincides with $AE$, it is unfolded

Then, $\angle DAG=$_____$°$

To construct an angle of $60°$, we need to draw first

Satish followed the steps given below

Step $1$: Construct an angle of $90°$.

Step $2$: Bisect the $90°$ angle.

Step $3$: Bisect one of the angles obtained in step $2$.

Which step is not required to construct a $45°$ angle?

A circular piece of paper is divided into two equal parts.

Next, the semi-circular piece is again folded so that the folds are equal.

This folded paper is folded once again, as drawn in the figure. Once again it is folded.

Now, it is unfolded

The angles formed are measured with a protractor.

If the portion of $22\frac{1}{2}°$ is cut off, the measure of $\angle COD=120°$.

Step 1: Let us draw any line segment $AB$ with scale pencil.

Step 2: Now, with centre $A$ and with any radius, lets draw an arc with compass, so that it cuts the line segment $AB$ at $C$.

Step 3: Next with centre $C$ and with the same radius, lets draw an arc which cuts the previous arc at $D$.

Step 4: Now, the points $D$ and $A$ are joined and extended. The angle is formed $\angle DAB=$ _____$°$.

Which of the following can be used to construct a $22.5°$ angle?

If the angle which should be bisected to construct a $30°$ angle is $x°$, then find the value of $x$.

Between $50°$ and $80°$, only _____ $°$ can be drawn with the help of compass and ruler. 

In the first square paper, the sides $AB, AD$ are folded about the corner point $A$, in a way as shown in figure $2$, so that the two folded parts overlaps each other perfectly.

When it is unfolded, we shall find the mark as in figure $3$

We find $\angle DAE=\angle EAF=\angle FAB=$_____$°$

Step $1$: Draw a ray $OA$.

Step $2$: With $O$ as centre and any convenient radius draw an arc $MN$ to cut $OA$ at $M$.

Step $3$: With $M$ as centre and the same radius draw an arc to cut $MN$ at $P$

Step $4$: With $P$ as centre and the same radius, draw an arc to cut $MN$ at $Q$.

Step $5$: Draw $OQ$ and produce it to $D$. An angle is constructed.

If the measure of angle formed is $x°$, then write the value of $x$.

Steps of construction:

1. Take any suitable radius and draw an arc which cuts ray $OA$ at point $P$. 

2. With point $P$ as centre and the same radius, mark an arc and name it as $F$. Again put your compasses at $F$ and with the same radius, draw an arc which intersects the initial arc at $E$.

3. Fix your compasses at $E$, draw an arc with a convenient radius. Repeat the process by putting the compasses at $F$ and let the two arcs intersect at $B$. Join $OB$. $\angle BOA=90°$.

4. Now, Bisect the obtained angle $BO$ and $OA$. Mark it as $OC$. $\angle COA=45°$.

5. Bisect $45°$ to get the required angle. The angles $OC$ and $OA$ are bisected and mark it as $OD$.

6. Hence, the required angle is $\angle DOA=$_____$°$. (Express in decimal)

A circular piece of paper is divided into two equal parts.

Next, the semi-circular piece is again folded so that the folds are equal.

This folded paper is folded once again, as drawn in the figure. Once again it is folded.

Now, it is unfolded

The angles formed are measured with a protractor.

If the $45°$ portion is cut off, what is the measure of the angle in the other portion in degrees? 

After constructing a $60°$ angle, if one of the arms of the angle is produced in the opposite direction, the angle formed is _____$°$

Which of the following angles can be constructed using ruler and compass?