Question

What’s the value of x? :/

Answer 1

`x = 27`

Explanation:

According to congruent chords and arcs theorem, if
`\overline{XY} \cong \overline{ZY}` then
`\arc{XY} \cong \arc{ZY}`.

This means that
`\arc{XY} = \arc{ZY} = (6x - 20) degrees`

Thus:

`\arc{XY} + \arc{ZY} + \arc{ZX} = 360` (full circle = 360°)

`\arc{XY} = (6x - 20)`

`\arc{ZY} = (6x - 20)`

`\arc{ZX} = 76`

Plug in the values into the equation

`(6x - 20) + (6x - 20) + 76 = 360`

`6x - 20 + 6x - 20 + 76 = 360`

Add like terms

`12x + 36 = 360`

Subtract 36 on both sides

`12x = 360 - 36`

`12x = 324`

Divide both sides by 12

`x = 27`