[tex]\huge\bold{Given :}[/tex]
Angle AOD = [tex]x[/tex] - 10°
Angle DOC = 3[tex]x[/tex] + 25°
Angle BOC = [tex]x[/tex] + 5°
[tex]\huge\bold{To\:find :}[/tex]
The value of [tex]x[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\sf\purple{The\:value\:of\:x\:is\:32°}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ ∠ AOD + ∠ DOC + ∠ BOC = 180°
➪ [tex]x[/tex] - 10° + 3[tex]x[/tex] + 25° + [tex]x[/tex] + 5° = 180°
Combining like terms, we have
➪ 5[tex]x[/tex] + 20° = 180°
➪ 5[tex]x[/tex] = 180° - 20°
➪ 5[tex]x[/tex] = 160°
➪ [tex]x[/tex] = [tex]\frac{160}{5}[/tex]
➪ [tex]x[/tex] = 32°
Therefore, the value of [tex]x[/tex] is 32°.
Now,
I) ∠ AOD = [tex]x[/tex] - 10° = 32° - 10° = 22°
2) ∠ DOC = 3[tex]x[/tex] + 25° = 3 x 32° +25° = 96° + 25° = 121°
3) ∠ BOC = [tex]x[/tex] + 5° = 32° + 5° = 37°
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
∠ AOD + ∠ DOC + ∠ BOC = 180°
✒ 22° + 121° + 37° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
