Question

Question 144
In rectangle READ, find $\angle EAR,\angle RAD$ and $\angle ROD$.

Answer 1

Given, a rectangle READ, in which $\angle ROE={60}^{\circ }$.
$\therefore \angle ROD={180}^{\circ }-{60}^{\circ }={120}^{\circ }$. [linear pair]
In $\Delta EOR,$
$\angle ROE+\angle DER+\angle ERA={180}^{\circ }$ [Angle sum property]
$\Rightarrow {60}^{\circ }+\angle ERA+\angle ERA={180}^{\circ }$ [$\because OE=OR$, hence $\angle DER=\angle ERA$]
$\Rightarrow 2\angle ERA={180}^{\circ }-{60}^{\circ }$
$\angle ERA=\frac{{120}^{\circ }}{2}={60}^{\circ }$
$\Rightarrow \angle RAD={60}^{\circ }$ [Alternate angles]

In rectangle READ, $\angle EAD={90}^{\circ }\Rightarrow \angle EAR+\angle RAD={90}^{\circ }\Rightarrow \angle EAR={90}^{\circ }-\angle RAD={90}^{\circ }-{60}^{\circ }={30}^{\circ }$