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Maria Walsh Maria Walsh Jan 15, 2021

In the adjoining figure, AB || DC. If x=find angle BCD, angle ABC, angle BAD and angle BDC.​

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Aɴsᴡᴇʀ

∵AB∥CD ᴀɴᴅ BD ɪs ᴛʀᴀɴsᴠᴇʀsᴀʟ.

∴x=40°(Aʟᴛᴇʀɴᴀᴛᴇ ᴀɴɢʟᴇs)

Nᴏᴡ ɪɴ △ABD

75°+ʏ+x=180°(Sᴜᴍ ᴏғ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ)

⇒ʏ=180°−75°−40°=180°−115°=65°

Nᴏᴡ ɪɴ △BCD

40°+(ʏ−30°)+ᴢ=180°(Sᴜᴍ ᴏғ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ)

∴ᴢ=180°−40°−35°=180°−75°=105°

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Jan 15, 2021
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