Question 514 Marks

Given below are the angles $x$ and $y$.

Without measuring these angles, construct :
$(i)\ (ii)\ (iii)$

Answer

(i) Steps of Construction :
Draw a line segment $BC$ of any suitable length.
With $B$ as the centre, draw an arc of any suitable radius. With the same radius, draw arcs with the vertices of given angles as centres. Let these arcs cut arms of the arc $x$ at points $P$ and $Q$ and arms of angle $y$ at points $R$ and $S$.
From the arc, with centre $B,$ cut $DE = PQ$ arc of $x$ and $EF = RS$ arc of $y$
Join $BF$ and produce up to point $A.$
Thus $\angle ABC = x + y$
(ii) Steps of Construction :

Proceed in exactly the same way as in part$(i)$
takes $DE = PQ =$ arc of $x.$
$EF = PQ =$ arc of $x$ and $FG = RS =$ arc of $y.$
Join $BG$ and produce it up to $A$.
Thus $\angle ABC = x + x+ y = 2x + y$​​​​​​​
(iii) Steps of Construction :

Proceed in exactly the same way as in $(ii)$
taking $DE = PQ = $ arc of $x$. and $EF = RS =$ arc of $y$ and $FG = RS =$ arc of $y$.
$4.$ Join $BF$ and produce up to point $A$.
Thus $\angle ABC = x + y + y = x + 2y$

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