Question

Find the value of x.

Answer 1

$\huge\bold{Given :}$

Angle AOD = $x$ - 10°

Angle DOC = 3$x$ + 25°

Angle BOC = $x$ + 5°

$\huge\bold{To\:find :}$

The value of $x$.

$\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}$

$\sf\purple{The\:value\:of\:x\:is\:32°}$

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}$

We know that,

$\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}$

➪ ∠ AOD + ∠ DOC + ∠ BOC = 180°

➪ $x$ - 10° + 3$x$ + 25° + $x$ + 5° = 180°

Combining like terms, we have

➪ 5$x$ + 20° = 180°

➪ 5$x$ = 180° - 20°

➪ 5$x$ = 160°

➪ $x$ = $\frac{160}{5}$

➪ $x$ = 32°

Therefore, the value of $x$ is 32°.

Now,

I) ∠ AOD = $x$ - 10° = 32° - 10° = 22°

2) ∠ DOC = 3$x$ + 25° = 3 x 32° +25° = 96° + 25° = 121°

3) ∠ BOC = $x$ + 5° = 32° + 5° = 37°

$\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}$

∠ AOD + ∠ DOC + ∠ BOC = 180°

✒ 22° + 121° + 37° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

$\boxed{Hence\:verified.}$

$\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}$

Answer 2

$\blue{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}}$

Find the value of x.

$\orange{\underline{\huge{\bold{\textit{\green{\bf{FORMULA}}}}}}}$

SUM OF ANGLES ON STRAIGHT LINE = 180°

$\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}$

$ANGLES\: R :-( x - 10)°,(3x + 25)°,(x + 5)°, \\ \\ ( x - 10)° + (3x + 25)° + (x + 5)° = 180 \\ 5x + 20 = 180 \\ 5x = 160 \\ x = \frac{160}{5} \\ x = 32°$

$\red{ANGLES R :-} \\ \pink{( x - 10)° = 32 - 10 = 22°} \\ \blue{ (3x + 25)° = 32 \times 3 + 25 = 96 + 25 = 121°}\\ \orange{(x + 5)° = 32 + 5 = 37°}$