[tex]\huge\bold{Given :}[/tex]
Angle ABC = 4x°
Angle BAC = x°
Angle BCA = 60°
[tex]\huge\bold{To\:find :}[/tex]
The value of x.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\green{x\:=\:24°}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ ABC + ∠ BAC + ∠ BCA = 180°
➪ 4x + x + 60° = 180°
➪ 5x + 60° = 180°
➪ 5x = 180° - 60°
➪ 5x = 120°
➪ x = [tex]\frac{120°}{5}[/tex]
➪ x = 24°
Therefore, the value of x is 24°.
Now, the three angles of the triangle are
∠ ABC = 4x = 4 x 24° = 96°
∠ BAC = x = 24°
∠ BCA = 60°
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
∠ ABC + ∠ BAC + ∠ BCA = 180°
✒ 96° + 24° + 60° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
(Note:- Kindly refer to the attached file.)
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
