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Properties of Triangles — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSProperties of Triangles3 Marks
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 $\angle \text{ECD}$
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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:
$3x + 2x + x = 180^\circ\ 6x = 180º$ Or, $x = 30^\circ …(i)$
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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