Question
In Fig. $\text{AC}\perp\text{CE}$ and $\angle\text{A}:\angle\text{B}:\angle\text{C}=3:2:1,$ find the value of $\angle\text{ECD}.$ 
✓
Answer
$\angle\text{A}:\angle\text{B}:\angle\text{C}=3:2:1$
Let the angles be $3x, 2x$ and $x$
$\Rightarrow 3x + 2x + x = 180^\circ $ [Angle sum property]
$\Rightarrow 6x = 180^\circ $
$\Rightarrow\text{x}=30=\angle\text{ACB}$
$\therefore\angle\text{ECD}=180^\circ-\angle\text{ACB}-90^\circ$[Linear pair]
$=180^\circ-30^\circ-90^\circ$
$=60^\circ$
$\therefore\angle\text{ECD}=60^\circ$
Let the angles be $3x, 2x$ and $x$
$\Rightarrow 3x + 2x + x = 180^\circ $ [Angle sum property]
$\Rightarrow 6x = 180^\circ $
$\Rightarrow\text{x}=30=\angle\text{ACB}$
$\therefore\angle\text{ECD}=180^\circ-\angle\text{ACB}-90^\circ$[Linear pair]
$=180^\circ-30^\circ-90^\circ$
$=60^\circ$
$\therefore\angle\text{ECD}=60^\circ$
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