Question

In ⨀O⨀O, an inscribed angle, ∠AZB∠AZB, and a central angle, ∠AOB∠AOB, intercept AB⌢AB⌢. © 2016 FlipSwitch. Created using GeoGebra. If m∠AZB=34°m∠AZB=34°, and mAB⌢=(6x+14)°mAB⌢=(6x+14)°, what is the value of xx?

Answer 1

The value of x is 9.

Explanation:

Given,

`m\widehat{AB}=(6x+14)^(\circ)`

`m\angle AZB=34^(\circ)`

By the central angle theorem,

`m\angle AZB=\frac{m\widehat{AB}}{2}`

By substituting the values,

`34=(6x+14)/(2)`

`68=6x+14`

`54=6x`

`\implies x=9`

Hence, the value of x is 9.