Question
Construct the following angles at the initial point of a given ray and justify the construction:
$i. 45^\circ$
$ii. 90^\circ$
$i. 45^\circ$
$ii. 90^\circ$
✓
Answer
$i.$Steps of construction:
$1.$ Draw a line segment $A B$ and produce $B A$ to $C$.
$2.$ Keeping $A$ as the center and any radius draw an arc which intersects $A C$ at $D$ and $A B$ at $E$
$3.$ Keeping $D$ and $E$ as center and radius more than half of $D E$ draw arcs which intersect each other at $F$.
$4.$ Join FA which intersects the arc in $(2)$ at $G$.
$5.$ Keeping $G$ and $E$ as center and radius more than half of $G E$ draw arcs which intersect each other at $H$.
$6$. Join $HA.$
Therefore $\angle\text{HBC}=45^\circ$
$ii.$ Steps of construction
$1.$ Draw a line segment $A B$.
$2.$ Keeping $A$ as the center and any radius draw an arc which intersects $A B$ at $C$.
$3.$ Keeping $C$ as center and the same radius draw an arc which intersects the previous arc at $D$.
$4.$ Keeping $D$ as the center and same radius draw an arc which intersects arc in $(2)$ at $E$.
$5.$ Keeping $E$ and $D$ as center and radius more than half of $ED$ draw arcs which intersect each other at $F$.
$6.$ Join $FA.$
Therefore $\angle\text{FAB}=90^\circ$
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