(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 $\Delta XYZ$ in which $\angle Y = 45^{\circ}$,$\angle Z = 60^{\circ}$ and $XY + YZ + ZX = 10 \, cm$. Write the steps of construction.

Medium

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Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $\angle B = 60^{\circ}$,$\angle C = 45^{\circ}$ and $AB + BC + AC = 12 \text{ cm}$.

Medium

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Construct a triangle $ABC$ in which $BC = 7.5\, cm$,$\angle B = 45^{\circ}$ and $AB - AC = 4\, cm$.

Medium

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Construct a right triangle whose base is $6\,cm$ and the sum of its hypotenuse and other side is $9\,cm$.

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Write True or False and give reasons for your answer.
An angle of $67.5^{\circ}$ can be constructed.

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

Similar Questions

Construct $\Delta XYZ$ in which $\angle Y = 45^{\circ}$,$\angle Z = 60^{\circ}$ and $XY + YZ + ZX = 10 \, cm$. Write the steps of construction.

Write True or False and give reasons for your answer.$A$ triangle $ABC$ can be constructed in which $\angle B = 60^{\circ}$,$\angle C = 45^{\circ}$ and $AB + BC + AC = 12 \text{ cm}$.

Construct a triangle $ABC$ in which $BC = 7.5\, cm$,$\angle B = 45^{\circ}$ and $AB - AC = 4\, cm$.

Construct a right triangle whose base is $6\,cm$ and the sum of its hypotenuse and other side is $9\,cm$.

Write True or False and give reasons for your answer.An angle of $67.5^{\circ}$ can be constructed.

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Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $\angle B = 60^{\circ}$,$\angle C = 45^{\circ}$ and $AB + BC + AC = 12 \text{ cm}$.

Write True or False and give reasons for your answer.
An angle of $67.5^{\circ}$ can be constructed.