Question

anybody help me to solve out this question please it's urgent
the one who answer right I will mark as brainlist or follow also

please help me......
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Answer 1

Answer

• ∠ DCE = 60°

Given

• Everything is in attachment ( question )

To Find

• $\rm \angle{DCE}$

Solution

Let angles be 3x , 2x , x respectively .

$\rm \angle{A}+\angle B+\angle C=180\ [Since,Angle\ in\ \Delta\ is\ 180^0]\\\\\implies \rm 3x+2x+x=180\\\\\implies \rm 6x\ =180\\\\\implies \rm x=30^0$

$\rm So, \angle A=3x=90^0 ,\angle B=2x=60^0,\angle C=x=30^0$

Since , ∠ BCA + ∠ ACD + ∠ DCE = 180° [ Straight line having 180° ]

⇒ ∠C + ∠ ACD + ∠ DCE = 180°

⇒ 30° + 90° + ∠ DCE = 180°

⇒ 120° + ∠ DCE = 180°

⇒ ∠ DCE = 180 - 120

⇒ ∠ DCE = 60°

Answer 2

$\large \bf \red{ {\underline { \underline{Given:-}}}}$

• $\sf In \: a \: \triangle ABC \: \angle A: \angle B :\: \angle C = 3:2:1$

• CD ⊥ AC

$\large \bf \blue{ {\underline { \underline{To\:Find:-}}}}$

• The measure of ∠ ECD

$\large \bf \green{ {\underline { \underline{Solution:-}}}}$

Let ∠BAC = 3x , ∠ABC = 2x and ∠ACB = x

As we know that the sum of angles in a triangle = 180°

$\sf \rightarrow\angle BAC+ \angle ABC + \angle ACB = 180 \degree$

$\sf \rightarrow3x + 2x + x = 180 \degree$

$\sf \rightarrow6x = 180 \degree$

$\sf \rightarrow x = \dfrac{180}{6}$

$\sf \rightarrow x =30 \degree$

$\sf \rightarrow \angle ACB = x =30 \degree$

As we know that the sum of angles on a straight line = 180°

$\sf \rightarrow \angle ACB + \angle ACD + \angle ECD$

$\sf \rightarrow 30 \degree + 90 \degree + \angle ECD = 180 \degree$

$\sf \rightarrow 120 \degree + \angle ECD = 180 \degree$

$\sf \rightarrow \angle ECD = 180 \degree - 120 \degree$

$\sf \rightarrow \angle ECD = 60 \degree$

Hence;

$\large \boxed{ \rm \purple{ \rightarrow \angle ECD = 60 \degree}}$