Question

The measure of three angles of a triangle are in the ratio 1:2:3, then the triangle is A. equilateral B. right angled C. isosceles D. obtuse angled​

Answer 1

Answer:

B

Step-by-step explanation:

x+2x+3x=180

6x=180

x=30

3x=90

therefore right angled triangle

Answer 2

Given :

• Measure of three angles of a triangle are in the ratio 1 : 2 : 3 .

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To find :

• Whether the given ratio forms equilateral, right angled, isosceles or obtuse angled triangle.

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Concept :

For this problem we must know the angles sum property of the triangles.

⠀⠀⌬ It states that the sum of three angles in a triangle must be 180°.

Knowing this we would form an equation for the given question and calculate the values of all three angles.

Finally after getting the values of angles we would be able to state what kind of triangle is formed.

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Solution :

So according to the question , as the measures of three angles of a triangle are in the ratio 1 : 2 : 3 , we will take the three angles as -

• x , 2x and 3x

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According to angle sum property of triangle -

$\sf\:x+2x+3x~=~180°$

$\sf\longrightarrow\:3x+3x~=~180°$

$\sf\longrightarrow\:6x~=~180°$

$\sf\longrightarrow\:x~=~\frac{180°}{6}$

$\sf\longrightarrow\:x~=~\cancel{\frac{180°}{6}}$

$\small{\underline{\boxed{\mathrm{\longrightarrow\:x~=~ 30°}}}}$

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Plugging the value of x in the assumed values of angles , we get -

⠀⠀⠀⌬ $\bf\:x~=~30°$

⠀⠀⠀⌬ $\bf\:2x~=~2 \times 30°~=~60°$

⠀⠀⠀⌬ $\bf\:3x~=~3 \times 30°~=~90°$

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$\sf\therefore\:Three~angles~are~30°~, ~60°~and~90°$

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Now coming to our final answer -

Observing the values we got for angles, we see that there is one 90° angle which denotes that the triangle formed would be a $\small{\mathfrak\blue{right~angled~triangle}}$.

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About triangles‎ :

• Equilateral triangle - The triangle whose length of all sides are equal is known as equilateral triangle.
• Right angled triangle - In a triangle, if the measure of any one angle be 90° it is classified as right angled triangle.
• Isosceles triangle - Among the three sides of a triangle if any of the two sides are equal in length, then the triangle is known as isosceles triangle.
• Obtuse triangle - If the measure of any of the one angle in a triangle be more than 90° , the triangle formed is known as obtuse triangle.

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