Respuesta :

If the inner arc is x, then the outer arc is 360 - x

[tex]70 = \frac{1}{2} ((360 - x) - x)[/tex]

[tex]70 = \frac{1}{2} (360 - 2x)[/tex]

[tex]70 = 180 - x[/tex]

[tex]x = 180 - 70[/tex]

[tex]x = 110 \textdegree[/tex]

Answer:

The correct option is a. The value of x is 110.

Step-by-step explanation:

From the given figure it is give

Radius and Tangents are perpendicular at the point of tangency.

It means

[tex]\angle OAP=\angle OBP=90^{\circ}[/tex]

AOBP is a quadrilateral. The sum of interior angles of a quadrilateral is 360.

[tex]\angle OAP+\angle AOB+\angle OBP+\angle APB=360^{\circ}[/tex]

[tex]90^{\circ}+x+90^{\circ}+70^{\circ}=360^{\circ}[/tex]

[tex]x+250^{\circ}=360^{\circ}[/tex]

[tex]x=110^{\circ}[/tex]

The value of x is 110. Therefore the correct option is a.

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