(D) $1$. Draw a ray $OA$. $2$. Using a compass,construct an angle of $90^{\circ}$ at point $O$. $3$. Construct an angle of $135^{\circ}$ at point $O$

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The resulting angle is $112.5^{\circ}$.

(D) $1$. Draw a ray $OA$. $2$. Using a compass,construct an angle of $90^{\circ}$ at point $O$. $3$. Construct an angle of $135^{\circ}$ at point $O$ (which is the angle bisector of $90^{\circ}$ and $180^{\circ}$). $4$. Now,bisect the angle between $90^{\circ}$ and $135^{\circ}$. $5$. The angle formed is $(90^{\circ} + 135^{\circ}) / 2 = 225^{\circ} / 2 = 112.5^{\circ}$.

Class 9 Mathematics Constructions Mix Examples - Constructions

Medium

Construct an angle of $112.5^{\circ}$ and write the steps of construction.

A
Draw a ray $OA$.
B
Construct $90^{\circ}$ and $135^{\circ}$ angles.
C
Bisect the angle between $90^{\circ}$ and $135^{\circ}$.
D
The resulting angle is $112.5^{\circ}$.

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Construct an angle of $112.5^{\circ}$ and write the steps of construction.

Similar Questions

Construct an angle of $157.5^{\circ}$ and write the steps of construction.

Construct a triangle $ABC$,in which $BC = 8 \, cm$,$\angle B = 75^{\circ}$ and $AB + AC = 15 \, cm$.

State whether the following statement is True or False and give reasons for your answer.$A$ triangle $ABC$ can be constructed in which $\angle B = 105^{\circ}, \angle C = 90^{\circ}$ and $AB + BC + AC = 10 \, cm$.

The construction of a triangle $ABC$,given that $BC = 3 \, cm$ and $\angle C = 60^{\circ}$,is possible when the difference of $AB$ and $AC$ is equal to: (in $cm$)

Draw an angle of $80^{\circ}$ with the help of a protractor. Then construct angles of $(i)$ $40^{\circ}$,$(ii)$ $160^{\circ}$,and $(iii)$ $120^{\circ}$.

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State whether the following statement is True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $\angle B = 105^{\circ}, \angle C = 90^{\circ}$ and $AB + BC + AC = 10 \, cm$.