Question

ABCD is a rectangle whose diagonals AC and BD intersect at O if angle OAB=46°find angleOBC

Answer 1

hello.. ☺
ᴇᴀᴄʜ ᴀɴᴅ ᴀɴɢʟᴇ ɪɴ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ɪs ᴇǫᴜᴀʟ ᴛᴏ 90°.

ᴅɪᴀɢᴏɴᴀʟs ᴏғ ʀᴇᴄᴛᴀɴɢʟᴇ ᴄᴜᴛs ᴇᴀᴄʜ ᴏᴛʜᴇʀ ɪɴᴛᴏ ᴛʜᴇɪʀ ʜᴀʟғ.

ᴀᴏ = ʙᴏ.

ᴡᴇ ᴋɴᴏᴡ,

ᴀɴɢʟᴇs ᴏᴘᴘᴏsɪᴛᴇ ᴛᴏ ᴇǫᴜᴀʟ sɪᴅᴇs ᴀʀᴇ ᴀʟsᴏ ᴇǫᴜᴀʟs.

sᴏ,

<ᴏʙᴀ = <ᴏᴀʙ

<ᴏʙᴀ = 46° ___ (1)

ᴡᴇ ᴋɴᴏᴡ,

<ᴀʙᴄ = <ᴏʙᴀ + <ᴏʙᴄ

90° = <46° + <ᴏʙᴄ

<ᴏʙᴄ = 44°.


thanks


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