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point o is the center if the circle. what is the value of x? mn and mp are tangent to

114
26
66
57

point o is the center if the circle what is the value of x mn and mp are tangent to 114 26 66 57 class=

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chikafujiwara

Answer:

[tex]x=66[/tex]

Step-by-step explanation:

Since  MN and MP are tangent to circle O, they create 90° angles at the points of intersection.

We also know that this is a quadralateral, so the interior angles add up to 360.

We can make an equation with this information.

[tex]114+90+90+x=360[/tex]

[tex]294+x=360[/tex]

[tex]x=66[/tex]

By property of tangent, the value of x is Option(C) 66° .

What are the properties of tangent ?

The properties of tangent are as follows -

  • Any tangent when intersect to a circle at the point, it subtends an angle of 90° at the interior segment.
  • The total sum of the interior angle of the intersection of tangent at the points is always equal to 360° .

How to find the given angle in the triangle ?

Given that point O is the center if the circle also given MN and MP are tangent to O.

Thus by the property of tangent, ∠OPM and ∠ONM is equal to 90° as both the tangents intersect at the points P and N .

Also from property, we know that -

⇒ ∠ONM + ∠OPM + 114° + x° = 360°

⇒  90° + 90° + 114° + x° = 360°

⇒ 294° + x° = 360°

∴  x = 360° - 294° = 66°

Therefore, by property of tangent, the value of x is Option(C) 66° .

To learn more about property of tangent, refer -

https://brainly.com/question/8705027

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