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Please help. I don't know any theorems that relate to this

Please help. I don't know any theorems that relate to this-example-1
User Termi
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1 Answer

24 votes
24 votes

Answer:

125°

Explanation:

In circle with center O.

  • BC is tangent at point B.
  • Draw segment OB
  • OB is radius

  • \implies OB\perp AB (Tangent theorem)

  • \implies\red{\bold{ m\angle OBC = 90\degree}}

  • m\angle AOB= 90\degree + 20\degree (By exterior angle theorem)

  • \implies m\angle AOB= 110\degree
  • OA = OB (radii of same circle)

  • \implies m\angle OAB = m\angle OBA = x \: (say) (By isosceles triangle theorem)

  • m\angle AOB + m\angle OAB +m\angle OBA=180\degree (By interior angle sum theorem of a triangle)

  • \implies 110\degree+ x +x=180\degree

  • \implies 2x =180\degree-110\degree

  • \implies 2x =70\degree

  • \implies x =35\degree

  • \implies \purple{\bold{m\angle OBA =35\degree}}

  • m\angle CBA=\red{\bold{m\angle OBC}} +\purple{\bold{m\angle OBA }}

  • m\angle CBA=90\degree + 35\degree

  • \huge{\orange{m\angle CBA=125\degree}}
User Shambu
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