Question
In Figure, $\text{AC}\bot\text{CE}$ and C $\angle \text{A}:\angle \text{B}:\angle \text{C}=3:2:1.$ Find the value of $\angle \text{ECD}$
✓
Answer
In the given triangle, the angles are in the ratio 3 : 2 : 1.
Let the angles of the triangle be 3x, 2x and x.
Because of the angle sum property of the triangle, we can say that:
3x + 2x + x = 180°
6x = 180º
Or,
x = 30° …(i)
Also, $\angle \text{ACB}+\angle \text{ACE}+\angle \text{ECD}=180^\circ$
$\text{x}+90^\circ+\angle \text{ECD}=180^\circ$ $(\angle \text{ACE}=90^\circ)$
$\angle \text{ECD}=60^\circ$ [From (i)]
Let the angles of the triangle be 3x, 2x and x.
Because of the angle sum property of the triangle, we can say that:
3x + 2x + x = 180°
6x = 180º
Or,
x = 30° …(i)
Also, $\angle \text{ACB}+\angle \text{ACE}+\angle \text{ECD}=180^\circ$
$\text{x}+90^\circ+\angle \text{ECD}=180^\circ$ $(\angle \text{ACE}=90^\circ)$
$\angle \text{ECD}=60^\circ$ [From (i)]
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