Question
Construct with ruler and compass, angle of measure $45^\circ$
✓
Answer
Construction of $45^\circ$.
In order to construct a $45-$degree angle, first, we will draw a $90$ degree angle using the below-mentioned steps:
$i.\ $Use a ruler to draw a line segment $OB ($of any length$)$
$ii.\ $Now use a compass and open it to any convenient radius. With $O$ as the center, draw an arc which cuts $OB$ at $X$
$iii.\ $With $X$ as the center and the radius as used in step $2,$ draw an arc which cuts the first arc a point $D.$
$iv.\ $With center as $D$ and the radius as used in step $2,$ draw another arc which cuts the first arc at a point $C$
$v.\ $With center as $C$ and $D$ and the radius as used in step $2,$ draw two arcs such that they cut each other at a point $E.$
$vi.\ $Join points $O$ and $E$ and extent $OE$ to a point $A$
$vii.\ $Angle $A O B$ formed above is of $90$ Degree. Inorder, to construct an angle of $45$ degree, we need to construct an angle bisector of angle $AOB,$ using the steps written below.
$viii.\ $Use compass, opened to any radius and with center as $O,$ draw an arc which cuts $OB$ at $P$ and $OA$ at $Q.$
$ix.\ $With center as $P$ and $Q$ and the radius as used in step $8 ,$ draw two arcs such that they cut each other at a point $F$
$x.\ $Join points $O$ and $F$ and extent $OF$ to a point $E.$
$xi.\ EO$ is the bisector of Angle $AOB$ i.e. Angle $AOE=$ Angle$ EOB = 1 \over 2$ of Angle $AOB = 45$ Degree
In order to construct a $45-$degree angle, first, we will draw a $90$ degree angle using the below-mentioned steps:
$i.\ $Use a ruler to draw a line segment $OB ($of any length$)$
$ii.\ $Now use a compass and open it to any convenient radius. With $O$ as the center, draw an arc which cuts $OB$ at $X$
$iii.\ $With $X$ as the center and the radius as used in step $2,$ draw an arc which cuts the first arc a point $D.$
$iv.\ $With center as $D$ and the radius as used in step $2,$ draw another arc which cuts the first arc at a point $C$
$v.\ $With center as $C$ and $D$ and the radius as used in step $2,$ draw two arcs such that they cut each other at a point $E.$
$vi.\ $Join points $O$ and $E$ and extent $OE$ to a point $A$
$vii.\ $Angle $A O B$ formed above is of $90$ Degree. Inorder, to construct an angle of $45$ degree, we need to construct an angle bisector of angle $AOB,$ using the steps written below.
$viii.\ $Use compass, opened to any radius and with center as $O,$ draw an arc which cuts $OB$ at $P$ and $OA$ at $Q.$
$ix.\ $With center as $P$ and $Q$ and the radius as used in step $8 ,$ draw two arcs such that they cut each other at a point $F$
$x.\ $Join points $O$ and $F$ and extent $OF$ to a point $E.$
$xi.\ EO$ is the bisector of Angle $AOB$ i.e. Angle $AOE=$ Angle$ EOB = 1 \over 2$ of Angle $AOB = 45$ Degree
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