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Geometrical Constructions — MATHS STD 6 — Question

Gujarat BoardEnglish MediumSTD 6MATHSGeometrical Constructions5 Marks
Question
Using a protractor, draw $\angle\text{BAC}$ of measure $45^\circ .$ Take a point $P$ in the interior of $\angle\text{BAC}.$ From $P$ draw line segments $PM$ and $PN$ such that $\text{PM}\perp\text{AB}$ and $\text{PN}\perp\text{AC},$ Measure $\angle\text{MPN}.$
✓

Answer

$i.\ $Draw a line segment $A$ on the line $L .$
$ii.\ $Take a protractor and place it on the segment $AC$ such that $AC$ coincides with the line of the diameter of the protractor and the middle point of the line coincides with point $A.$
$iii.\ $Counting from the right side, mark a point as $B$ at the point of $45^\circ $ of protractor and draw a line segment $AB.$
$iv.\ $Take a convenient radius with $P$ as centre, construct an arc intersecting the line segments $AB$ at $T$ and $Q$ and $AC$ at $R$ and $S.$
$v.\ $Using the same radius and with $T$ and $Q$ as centres, construct two arcs intersecting at $G$ on the other side.
$vi.\ $Using the same radius and with $R$ and $S$ as centres, construct two arcs intersecting at $H$ on the other side.
$vii.\ $Join $PG$ and $PH$ which intersects $AB$ and $AC$ at $M$ and $N,$ respectively.
On measuring $\angle\text{MPN}$ using a protractor, we get it equal to $135^\circ .$

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