Question

If all the angles of the triangle are in ratio of 2:3:5. then find out measurement of all the
angles. Identify the type of triangle.​

Answer 1

Given : ↴

$\sf \: All \: the \: angles \: of \: the \: \triangle \: are \: in \: ratio \: of \: 2 \: : \: 3 \: : \: 5$

To find : ↴

$\sf \longrightarrow \: Value \: of \: each \: angle.$

$\sf \longrightarrow \: Indentify \: the \: type \: of \: type \: of \: \triangle .$

So, Let's Start : ↴

$\sf \: \purple{We \: know \: that \: Sum \: of \: all \: the \: \triangle \: is \: 180 \degree }$

$\sf \: So, \: Side_1 \: + \: Side_2 \: + \: Side_3 \: = \: 180 \degree$

$\sf \: \longrightarrow \: 2x \: + \: 3x \: + \: 5x \: = \: 180 \degree$

$\sf \: \longrightarrow \: 10x \: = \: 180 \degree$

$\sf \: \longrightarrow \: x \: = \: \dfrac{180 \degree}{10}$

$\sf \: \large \longrightarrow \: x \: = \: 180 \degree$

$\sf \: So, \: 2x \: = \: 2 \: \times \: 18 \: = \: 36\degree$

$\sf \: 3x \: = \: 3\: \times \: 18 \: = \: 54\degree$

$\sf \: 5x \: = \: 5\: \times \: 18 \: = \: 90 \degree$

$\sf \: \green{ So, \: the \: angles \: of \: the \: triangle \: are \: 36\degree, \: 54\degree, \: 90\degree.}$

Answer = 36°, 54°, 90°

One angle of the triangle is 90°, So, it is a Right angle triangle.

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$\bf \: \underline{ Extra\: information}\::$ ↴

A triangle is a simplest form of polygon and it have three sides in it.

$\bf \: \underline{\red{Properties \: of \: Triangle} \: :}$ ↴

(1). A triangle always have three sides, three angles, and three vertices.

(2). The sum of the length of any two sides of a triangle is always greater than the length of the third side. (Angle sum property of a triangle)

(3). The sum of all internal angles of a triangle is always equal to 180°.

(4). The side opposite to the largest angle of a triangle is the largest side.

(5). Any exterior angle of the triangle is equal to the sum of its interior opposite angles. (Exterior angle property of a triangle)

Answer 2

★ Given :

• If all the angles of the triangle are in ratio of 2:3:5.

★ To find :

• Find out measurement of all the angles.
• Identify the type of triangle.

★ Solution :

Let the angles be 2x ,3x and 5x

• In the question it is given that Angles of traingle are in Ratio. so let the angles be 2x,3x and 5x.

• Sum of all angles of triangle is 180°

Let's Find out..!

∠1 + ∠2 +∠3 = 180°

➤ 2x + 3x + 5x = 180°

➤ 10x = 180°

➤ x = 180/10

➤ x = 18°

Now finding angles.

✰ x = 18°

✰ 3x = 3 × 18 = 54°

✰ 5x = 5 × 18 = 90°

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18°, 54°, 90° are the angles of triangle.

The angle who measures 90° is right angle traingle, so this is right angle traingle.

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