Question

in the given figure certain meansures of angles with the help of this information show that ray BA parallel ray EF​

Answer 1

Answer:

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(ɪ) ꜱɪɴᴄᴇ, ʀᴩ ɪꜱ ᴀ ꜱᴛʀᴀɪɢʜᴛ ʟɪɴᴇ ᴀɴᴅ ʀᴀy ʜᴅ ꜱᴛᴀɴᴅꜱ ᴏɴ ɪᴛ, ᴛʜᴇɴ

∠ʀʜᴅ + ∠ᴅʜᴩ = 180∘    (ᴀɴɢʟᴇꜱ ɪɴ ᴀ ʟɪɴᴇᴀʀ ᴩᴀɪʀ)

⇒∠ʀʜᴅ + 85∘ = 180∘

⇒∠ʀʜᴅ = 180∘ − 85∘ = 95∘ 

(ɪɪ) ꜱɪɴᴄᴇ ᴛʜᴇ ꜱᴛʀᴀɪɢʜᴛ ʟɪɴᴇꜱ ʀᴩ ᴀɴᴅ ᴅᴋ ɪɴᴛᴇʀꜱᴇᴄᴛ ᴀᴛ ʜ, ᴛʜᴇɴ

∠ᴩʜɢ =  ∠ʀʜᴅ    (ᴠᴇʀᴛɪᴄᴀʟʟy ᴏᴩᴩᴏꜱɪᴛᴇ ᴀɴɢʟᴇꜱ)

⇒∠ᴩʜɢ = 95∘

(ɪɪɪ) ꜱɪɴᴄᴇ, ᴛʜᴇ ʟɪɴᴇ ʀᴩ || ʟɪɴᴇ ᴍꜱ ᴀɴᴅ ʟɪɴᴇ ᴅᴋ ɪꜱ ᴛʜᴇɪʀ ᴛʀᴀɴꜱᴠᴇʀꜱᴀʟ ɪɴᴛᴇʀꜱᴇᴄᴛɪɴɢ ᴛʜᴇᴍ ᴀᴛ ʜ ᴀɴᴅ ɢ, ᴛʜᴇɴ

∠ʜɢꜱ = ∠ᴅʜᴩ    (ᴄᴏʀʀᴇꜱᴩᴏɴᴅɪɴɢ ᴀɴɢʟᴇꜱ)

⇒∠ʜɢꜱ = 85∘

(ɪᴠ) ꜱɪɴᴄᴇ, ᴛʜᴇ ꜱᴛʀᴀɪɢʜᴛ ʟɪɴᴇꜱ ᴍꜱ ᴀɴᴅ ᴅᴋ ɪɴᴛᴇʀꜱᴇᴄᴛ ᴀᴛ ɢ, ᴛʜᴇɴ

∠ᴍɢᴋ =  ∠ʜɢꜱ    (ᴠᴇʀᴛɪᴄᴀʟʟy ᴏᴩᴩᴏꜱɪᴛᴇ ᴀɴɢʟᴇꜱ)

⇒∠ᴍɢᴋ = 85∘