If angles of a triangles are in the ratio 2:3:5, the value of the greatest angles is:
Answers
Answered by
7
- ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ 2:3:5.
:
- ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ=?
:
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}}} \huge\mathfrak\red{\underline\orange{\underline\red{x=18}}}](https://tex.z-dn.net/?f=%5Chuge%5Cmathfrak%5Cred%7B%5Cunderline%5Corange%7B%5Cunderline%5Cred%7Bx%3D18%7D%7D%7D)
ᴛʜᴇʀᴇғᴏʀᴇ,
ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ɢʀᴇᴀᴛᴇsᴛ ᴀɴɢʟᴇ ɪs
5x=5(18)=90°
Answered by
12
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°.
Similar questions
History,
1 month ago
Economy,
1 month ago
Business Studies,
1 month ago
English,
2 months ago
Biology,
2 months ago
Computer Science,
7 months ago
Biology,
7 months ago