Question

In a triangle, if an exterior angle is
${130}^{.}$

and one of the opposite angles is
${60}^{.}$
, find the other angles​

Answer 1

Answer:

ɪɴ ∆ʟᴇ

ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ = 130°

ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇ = 60°

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

sᴜᴍ ᴏғ ᴛᴡᴏ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇs = ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ

ʟᴇᴛ ᴏᴘᴘᴏsɪᴛᴇ ᴀɴɢʟᴇ ʙᴇ x ᴀɴᴅ ʏ

ᴀɴᴅ ʏ = 60°

ᴛʜᴇɴ,

x + ʏ = 130°

x + 60° = 130°

x = 130° - 60°

x = 70°

ᴛʜᴇɴ ᴛᴡᴏ ᴀɴɢʟᴇs ᴀʀᴇ 60° ᴀɴᴅ 70°

ᴛʜᴇɴ ʙʏ ᴀɴɢʟᴇ sᴜᴍ ᴘʀᴏᴘᴇʀᴛʏ

ʟᴇᴛ ᴀɴᴏᴛʜᴇʀ ᴀɴɢʟᴇ ʙᴇ ᴢ

x + ʏ + ᴢ = 180°

70° + 60° + ᴢ = 180°

130° + ᴢ = 180°

ᴢ = 180° -130°

ᴢ = 50°

ᴀʟʟ ᴀɴɢʟᴇs ᴀʀᴇ 60° , 70° ᴀɴᴅ 50°