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Angle Sum Property

In ABC, ∠ C...

Question

In $△ A B C, ∠ C = 3 ∠ A$ and $∠ B = 2 ∠ A$ . Which of the following is $△ A B C$ ?

Equilateral

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Isosceles

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Obtuse angled

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Right angled

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Solution

The correct option is D Right angled
Let $∠ A = x$
$\Rightarrow ∠ C = 3 x$ and $∠ B = 2 x$
Using angle sum property of triangle
$x + 2 x + 3 x = 180^{\circ} \Rightarrow 6 x = 180^{\circ} \Rightarrow x = 30^{\circ}$
So the angles are
$∠ A = x = 30^{\circ} ∠ B = 2 x = 2 \times 30^{\circ} = 60^{\circ} ∠ C = 3 x = 3 \times 30^{\circ} = 90^{\circ}$
One of the angle is right angle . So the triangle is right triangle.

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Similar questions

Q. In a

△ A B C

, if

cot A \cdot cot C = \frac{1}{2}

and

cot B \cdot cot C = \frac{1}{18}

, then which of the following is/are true?

Q. If in triangle ABC, right angled at

B, s - a = 3

and

s - c = 2

, then which of the following is correct?

Q. Observe the following Statements:

I)

Δ A B C, b {cos}^{2} \frac{C}{2} + c {cos}^{2} \frac{B}{2} = s

I I)

Δ A B C, cot \frac{A}{2} = \frac{b + c}{a} \Rightarrow

Triangle is right angled.
Which of the following is correct :

$Δ A B C$ is congruent to $Δ R Q P$ , that is $Δ A B C ≅ Δ R Q P$ . If $∠ C$ and $∠ P$ are the smallest angles in $Δ A B C$ and $Δ R Q P$ , then which of the following is not true?

Q. Consider a

△ A B C

whose sides

a, b

and

c

are such that

a^{2}, b, c^{2}

are in

G . P .,

then which of the following statement(s) is/are correct ?
(where

a, b, c

are sides of

△ A B C

opposite to

∠ A, ∠ B

and

∠ C

respectively)

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In △ABC,∠C=3∠A and ∠B=2∠A. Which of the following is △ABC?

The correct option is D Right angledLet ∠A=x⇒∠C=3x and ∠B=2xUsing angle sum property of trianglex+2x+3x=180∘⇒6x=180∘⇒x=30∘So the angles are ∠A=x=30∘∠B=2x=2×30∘=60∘∠C=3x=3×30∘=90∘One of the angle is right angle . So the triangle is right triangle.

In $△ A B C, ∠ C = 3 ∠ A$ and $∠ B = 2 ∠ A$ . Which of the following is $△ A B C$ ?