[tex]\huge\bold{Given :}[/tex]
Angle CBA = 60°
Angle BAC = 40°
Angle BCA = [tex]x[/tex]
[tex]\huge\bold{To\:find :}[/tex]
The measure of angle [tex]x[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:80°}}}}}}[/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]
➪ ∠ CBA + ∠ BAC + ∠ BCA = 180°
➪ 60° + 40° + [tex]x[/tex] = 180°
➪ 100° + [tex]x[/tex] = 180°
➪ [tex]x[/tex] = 180° - 100°
➪ [tex]x[/tex] = 80°
Therefore, the measure of angle [tex]x[/tex] is 80°.
Now, the three angles of the triangle are 60°, 40° and 80° respectively.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
∠ CBA + ∠ BAC + ∠ BCA = 180°
✒ 60° + 40° + 80° = 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{ヅ}}}}}[/tex]
