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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?

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Answer:

The value of x is 9.

Step-by-step explanation:

Given,

[tex]m\widehat{AB}=(6x+14)^{\circ}[/tex]

[tex]m\angle AZB=34^{\circ}[/tex]

By the central angle theorem,

[tex]m\angle AZB=\frac{m\widehat{AB}}{2}[/tex]

By substituting the values,

[tex]34=\frac{6x+14}{2}[/tex]

[tex]68=6x+14[/tex]

[tex]54=6x[/tex]

[tex]\implies x=9[/tex]

Hence, the value of x is 9.

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