Question

What’s the value of x? :/

Answer 1

Answer:

$x = 27$

Step-by-step 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

$x = 27$