[tex]\huge\bold{Given:}[/tex]
Angle AOB = x + 4
Angle BOC = 3x + 2
Angle AOC =90° ( ∵ it is right angle )
[tex]\huge\bold{To\:find:}[/tex]
The value of "x".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\blue{x\:=\:21°}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
Since it is right-angle,
[tex]Sum \: of \: angles \: = 90°[/tex]
[tex]\longrightarrow{\green{}}[/tex] x + 4 + 3x + 2 = 90°
[tex]\longrightarrow{\green{}}[/tex] x + 3x + 4 + 2 = 90°
[tex]\longrightarrow{\green{}}[/tex] 4x + 6 = 90°
[tex]\longrightarrow{\green{}}[/tex] 4x = 90° - 6
[tex]\longrightarrow{\green{}}[/tex] 4x = 84°
[tex]\longrightarrow{\green{}}[/tex] x = [tex]\frac{84°}{4}[/tex]
[tex]\longrightarrow{\green{}}[/tex] x = 21°
[tex]\sf\blue{Therefore,\:the\:value\:of\:x\:is\:21°.}[/tex]
Now, the two angles are
∠ AOB = x + 4 = 21° + 4 = 25°
∠ BOC = 3x + 2 = 3 x 21° + 2 = 63° + 2 = 65°
[tex]\huge\bold{To\:verify :}[/tex]
➡ ∠ AOB + ∠ BOC = ∠ AOC
➡ 25° + 65° = 90°
➡ 90° = 90°
➡ L. H . S. = R. H. S
Hence verified. ✔
(Note:- Kindly refer to the attached file.)
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
