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` =
`(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{♡}}}}}`