Question

Draw an angle of measure ${45^o}$and bisect it.

Answer 1

An angle is the figure formed by two rays, called the sides of the angle sharing a common endpoint, called a vertex of the angle. To do this construction,first draw a straight line segment of suitable length and then proceed

Complete step by step solution:
(1) Draw a line segment of length $3cm$ and name it as AB

(2) Taking $A$ as the centre with suitable radius, mark an arc which intersects $AB$ at $C$.

(3) Now, taking $C$ as the centre and with the same radius cut the point $C$ at $D$. Taking $D$ as the centre and with the same radius, draw another arc intersecting the same arc at $E$.

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(4) Now, taking $D\,and\,\,E$ as centres and with the same radius mark two arcs intersecting each other at $G$. $\angle GAB$ is equal to ${90^o}$.

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(5) Draw the bisector of $\angle GAB$ i.e.
$\angle HAB =$ $\dfrac{1}{2} \times 90 = {45^o}$

(6) Draw the bisector of $\angle GAH,\angle IAB = \dfrac{1}{2} \times {45^o} = 22.5$.
Therefore,$\angle IAB = {22.5^o}$

Note: Students must be careful while using compass and ruler. Also while marking the angle, one must be cautious and mark the angles appropriately.Even a small mistake can lead to construction going wrong.