Question

In this picture, m∠XOZ = 70° and m∠YOZ = 37°. If m∠XOY = (5x + 16)°, what is the value of x?

Answer 1

`\huge\bold{Given :}`

m∠XOZ = 70°

m∠YOZ = 37°

m∠XOY = ( 5x + 16 )°

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

The value of x°.

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

`{\boxed{\mathcal{\red{The\:value\:of\: x° \:is\:3.4° .\:}}}}`✅

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

We know that,

`\sf\pink{m∠XOZ\:=\:m∠YOZ\:+\:m∠XOY}`

➪ 70° = 37° + 5x° + 16°

➪ 5x° + 53° = 70°

➪ 5x° = 70° - 53°

➪ 5x° = 17°

➪ x° =
`(17° )/(5)`

➪ x° = 3.4°

`\sf\red{Therefore, \:the\: value \:of \:x°\: is \:3.4°.}`

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

✒ 70° = 37° + 5 x 3.4° + 16°

✒ 70° = 37° + 17° + 16°

✒ 70° = 70°

✒ L. H. S. = R. H. S.

`\boxed{Hence\:verified.}`

`\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}`

Answer 2

x = 3.4

Explanation:

You have the value of xoz = 70, yoz = 37 and xoy = 5x+16

Set your formula up as

xoz = yoz + xoy

70 = 37 + 5x + 16

70 - 37 - 16 = 5x

17 = 5x

17 / 5 = x

3.4 = x