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
⇒ 3x + 2x + x = 180° [Angle sum property]
⇒ 6x = 180°
$\Rightarrow\text{x}=30=\angle\text{ACB}$
$\therefore\angle\text{ECD}=180^\circ-\angle\text{ACB}-90^\circ$ ° [Linear pair]
$=180^\circ-30^\circ-90^\circ$
$=60^\circ$
$\therefore\angle\text{ECD}=60^\circ$
⇒ 3x + 2x + x = 180° [Angle sum property]
⇒ 6x = 180°
$\Rightarrow\text{x}=30=\angle\text{ACB}$
$\therefore\angle\text{ECD}=180^\circ-\angle\text{ACB}-90^\circ$ ° [Linear pair]
$=180^\circ-30^\circ-90^\circ$
$=60^\circ$
$\therefore\angle\text{ECD}=60^\circ$
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