In the given figure- interior angles of - ABC are in the ratio -A- -B -C-3-2-1 Side BC is produced to D and EC- AC- Find -DCE-

Let ∠A=3x ∠B=2x and ∠C=x. [∠A : ∠B: ∠C=3: 2: 1] In Δ ABC, ∠A+∠B+∠C=180^∘ ⇒ 3x+2x+x=180^∘ [Sum of interior angles of a triangele is 180^∘] ⇒ 6x=180^∘ ⇒ x= 30 ...

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Standard X

Mathematics

Similar Triangles

In the given ...

Question

In the given figure, interior angles of $Δ A B C$ are in the ratio $∠ A : ∠ B : ∠ C = 3 : 2 : 1$ Side BC is produced to D and $E C ⊥ A C . F i n d ∠ D C E .$

30 degrees

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75 degrees

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60 degrees

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100 degrees

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Solution

The correct option is C
60 degrees
Let
$∠ A = 3 x ∠ B = 2 x a n d ∠ C = x . [∠ A : ∠ B : ∠ C = 3 : 2 : 1] I n Δ A B C, ∠ A + ∠ B + ∠ C = 180^{\circ} \Rightarrow 3 x + 2 x + x = 180^{\circ} [Sum of interior angles of a triangele is 180^{\circ}] \Rightarrow 6 x = 180^{\circ} \Rightarrow x = 30^{\circ} Since exterior angle is equal to the sum of two interior opposite angle, ∴ ∠ A C D = ∠ A + ∠ B \Rightarrow ∠ A C E + ∠ D C E = 90^{\circ} + 60^{\circ} \Rightarrow ∠ 90^{\circ} + ∠ D C E = 150^{\circ} \Rightarrow ∠ D C E = 60^{\circ}$

So, option c is correct.

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In the given figure, interior angles of ΔABC are in the ratio ∠A: ∠B :∠C=3:2:1 Side BC is produced to D and EC⊥ AC. Find ∠DCE.

In the given figure, interior angles of $Δ A B C$ are in the ratio $∠ A : ∠ B : ∠ C = 3 : 2 : 1$ Side BC is produced to D and $E C ⊥ A C . F i n d ∠ D C E .$