Question

ᴛʜᴇ ᴛʜʀᴇᴇ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇs ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 1:2:3 . ғɪɴᴅ ᴛʜᴇ ᴀʟʟ ᴛʜᴇ ᴀɴɢʟᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇs .​

Answer 1

Answer :

›»› The all three angles of a triangle is 30°, 60°, 90° respectively.

Given :

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

To Find :

• The all angles of a triangle = ?

Solution :

Let us assume that, the angles of a triangle is "1x", "2x", and "3x" respectively.

As we know that

The sum of all three angles of a triangle is 180°. This statement is called angles sum property of triangle.

According to the given question,

→ 1x + 2x + 3x = 180

→ 3x + 3x = 180

→ 6x = 180

→ x = 180/6

→ x = 30

Therefore,

The all three angles of a triangle will be,

• 1x = 1 * 30 = 30°.
• 2x = 2 * 30 = 60°.
• 3x = 3 * 30 = 90°.

Hence, the all three angles of a triangle is 30°, 60°, 90° respectively.

Verification :

The sum of all three angles of a triangle is 180°.

→ 30 + 60 + 90 = 180

→ 90 + 90 = 180

→ 180 = 180

Clearly, LHS = RHS.

Here both the conditions satisfy, so our answer is correct.

Hence Verified !

Answer 2

Answer:

$\huge \bf \: Given$

• The sides of a triangle are in ratio = 1:2:3

$\huge \bf \: To \: find$

The sides

$\huge \bf \: Solution$

Let us assume that the sides to be x

As we know that sum of all sides of triangle is 180

Therefore,

$\sf \: 1x + 2x + 3x = 180$

Now,

Finding value of x

$\sf \: 6x = 180$

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

$\sf \: x \: = 30$

Therefore sides will be

$\tt \: x = 30$

$\tt \: 2x = 2(30) = 60$

$\tt \: 3x = 3(30) = 90$

Let's verify

$\rm30 + 60 + 90 = 180$

$\rm \: 180 = 180$

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