[tex]\huge\bold{Given:}[/tex]
Angle BOC = 65°
Angle AOC =90° ( ∵ it is right angle )
[tex]\huge\bold{To\:find:}[/tex]
The measure of angle AOB [tex]"x°"[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\blue{x°\:=\:25°}}[/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] [tex]x°[/tex] + 65° = 90°
[tex]\longrightarrow{\green{}}[/tex] [tex]x°[/tex] = 90° - 65°
[tex]\longrightarrow{\green{}}[/tex] [tex]x°[/tex] = 25°
[tex]\sf\blue{Therefore,\:the\:measure\:of\:x°\:is\:25°.}[/tex]
[tex]\huge\bold{To\:verify :}[/tex]
➡ ∠ AOB + ∠ BOC = ∠ AOC
➡ 25° + 65° = 90°
➡ 90° = 90°
➡ L. H. S. = R. H. S
Hence verified. ✔
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
