Question
Construct the following and give justification: A triangle if its perimeter is $10.4\ cm$ and two angles are $45^\circ $ and $120^\circ $
✓
Answer
Steps of construction,
$1.$ Draw $XY = 10.4\ cm$
$2.$ Draw $\angle\text{LXY}=45^\circ$ and $\angle\text{MYX}=120^\circ$ with the help of protractor.
$3.$ Draw angle bisector $\angle\text{LXY}.$
$4.$ Draw angles bisector of $\angle\text{MYX}$ such that it meets the angle bisector of $\angle\text{LXY}$ at point $A.$
$5.$ Draw the perpendicular bisector of $AX$ such that it meets $XY$ at $B.$
$6.$ Draw the perpendicular bisector of $AY$ such that it meets $XY $at $C$.
$7.$ Join $AB$ and $AC$.
Thus $\text{ABC}$ is the required triangle.
$1.$ Draw $XY = 10.4\ cm$
$2.$ Draw $\angle\text{LXY}=45^\circ$ and $\angle\text{MYX}=120^\circ$ with the help of protractor.
$3.$ Draw angle bisector $\angle\text{LXY}.$
$4.$ Draw angles bisector of $\angle\text{MYX}$ such that it meets the angle bisector of $\angle\text{LXY}$ at point $A.$
$5.$ Draw the perpendicular bisector of $AX$ such that it meets $XY$ at $B.$
$6.$ Draw the perpendicular bisector of $AY$ such that it meets $XY $at $C$.
$7.$ Join $AB$ and $AC$.
Thus $\text{ABC}$ is the required triangle.
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