Question

If angles of a triangles are in the ratio 2:3:5, the value of the greatest angles is:

Answer 1

$\huge\mathfrak\red{\underline\orange{\underline\purple{Given}}}$

• ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 2:3:5.

$\huge\mathfrak\red{\underline\orange{\underline\purple{To Find}}}$:

• ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ=?

$\huge\mathfrak\red{\underline\orange{\underline\purple{Solution}}}$:

ʟᴇᴛ ᴛʜᴇ ᴄᴏᴍᴍᴏɴ ᴍᴜʟᴛɪᴘʟᴇ ʙᴇ x.

sɪɴᴄᴇ ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

sᴜᴍ ᴏғ ᴀʟʟ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪs 180°.

: . 2x+3x+5x=180°

: . 10x=180°

: .$\huge\mathfrak\red{\underline\orange{\underline\red{x=18}}}$

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ ɪs

5x=5(18)=90°

Answer 2

Answer:

The greatest angle of the triangle is 90°.

Step-with-Step Explanation :

Given :

• Ratio of the angles are 2:3:5.

To find?

• The greatest angle of the triangle.

Knowledge required :

• The sum of all the angles of a triangle is 180°.

Let 2x, 3x & 5x be the angles of the triangle.

Now,

2x + 3x + 5x = 180°

⇒5x + 5x = 180°

⇒10x = 180°

⇒x = 180°/10

⇒x = 18°

.°. x = 18°

Finding the angles :

2x = 2 × 18° → 36°

3x = 3 × 18° → 54°

5x = 5 × 18° → 90°

Hence, the greatest angle of the triangle is 90°.