QUESTION :
Find the given value of each angle for the following supplementary angles must add up to 180
[tex]\Large{\underline{\mathcal{ Given : }}}[/tex]
- one angle = (5x-13)°
- another angle = (11x+65)°
[tex]\Large{\underline{\mathcal{Tofind : }}}[/tex]
[tex]\Large{\underline{\mathcal{Solution : }}}[/tex]
➱ᴛʜᴇ ᴛᴡᴏ ᴀɴɢʟᴇs ʟɪᴇs ᴏɴ ᴛʜᴇ sᴀᴍᴇ ʟɪɴᴇ
➱ѕσ ѕυм σƒ вσтн тнє αηgℓєѕ = 180°
therefore ,
⤳(5x-13)° + (11x+65)° = 180°
⤳5x -13° + 11x + 65° = 180°
⤳16x + 52° = 180°
⤳16x = 180° - 52°
⤳16x = 128°
⤳x = 128 /16
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\boxed{\sf{ x = \frak{\red{ 8 }}}}}[/tex]
hence ,
the two angles will be
⇛ᴏɴᴇ ᴀɴɢʟᴇ :
➛(5x-13)°
➛5(8) - 13
➛40 - 13
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\boxed{\sf{ᴏɴᴇ\: ᴀɴɢʟᴇ = \frak{\red{ 27° }}}}}[/tex]
⇛ᴀɴᴏᴛʜᴇʀ ᴀɴɢʟᴇ :
➛ (11x+65)°
➛11(8)+65
➛88 + 65
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\boxed{\sf{ᴀɴᴏᴛʜᴇʀ\: ᴀɴɢʟᴇ = \frak{\red{ 153° }}}}}[/tex]
