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

Answer:

The value of x is 9.

Step-by-step 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,

$34=\frac{6x+14}{2}$

$68=6x+14$

$54=6x$

$\implies x=9$

Hence, the value of x is 9.