Question

$\left(a\right).$Construct a $30°$ angle.

$\left(b\right).$ Construct a $15°$ angle.

$\left(a\right)$

Short answer

The figure is,

Step-by-step solution

Step 1. Given information.

The angle to draw is $30°$.

Step 2. Concept used.

To construct the angles of $30°$,

consider the following ways,

Draw the line $\overrightarrow{AB}$.

Place the compass vertex on the angle’s vertex $A$.

Set the compass to any convenient radius and draw an arc on $AB$ at some point.

Mark that point as $L$with same radius.

With centre as $L$ and radius more than $LM$ draw an arc.

With centre $M$ and without changing the radius of the compassintersect the arc at point $N$.

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

Step 3. Construct the figure.

The figure is,

Therefore, the required construction in which angle between two lines is $30°$.

$\left(b\right)$

The figure is,

Step 1. Given information.

The angle to draw is $15°$.

Step 2. Concept used.

To construct the angles of $15°$,

consider the following ways,

Draw the line $\overrightarrow{AB}$

Place the compass on the angle’s vertex $A$.

Set the compass to any convenient radius and draw an arc on $AB$at some point.

Mark that point as $L$.

With centre $L$ and radius more than $LM$ draw an arc.

With centre $M$ and without changing the radius of the compassintersect the arc at point $N$.

Draw a line from $A$ to where the arcs intersect and angle constructed is $30°$.

With centre $Q$and radius more than $QM$ draw an arc.

With centre $M$and without changing the radius of the compassintersect the arc at point $P$.

Draw a line passing through $A$ and $P$to construct an angle of $15°$.

Step 3. Construct the figure.

The figure is,

Therefore, the required construction in which angle between two lines is $15°$.