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Answer :

Hrishiigo

Answer:

125°

Step-by-step explanation:

In circle with center O.

  • BC is tangent at point B.
  • Draw segment OB
  • OB is radius
  • [tex]\implies OB\perp AB[/tex] (Tangent theorem)
  • [tex]\implies\red{\bold{ m\angle OBC = 90\degree}}[/tex]
  • [tex]m\angle AOB= 90\degree + 20\degree[/tex] (By exterior angle theorem)
  • [tex]\implies m\angle AOB= 110\degree[/tex]
  • OA = OB (radii of same circle)
  • [tex]\implies m\angle OAB = m\angle OBA = x \: (say)[/tex] (By isosceles triangle theorem)
  • [tex]m\angle AOB + m\angle OAB +m\angle OBA=180\degree[/tex] (By interior angle sum theorem of a triangle)
  • [tex]\implies 110\degree+ x +x=180\degree[/tex]
  • [tex]\implies 2x =180\degree-110\degree[/tex]
  • [tex]\implies 2x =70\degree[/tex]
  • [tex]\implies x =35\degree[/tex]
  • [tex]\implies \purple{\bold{m\angle OBA =35\degree}}[/tex]
  • [tex]m\angle CBA=\red{\bold{m\angle OBC}} +\purple{\bold{m\angle OBA }}[/tex]
  • [tex]m\angle CBA=90\degree + 35\degree[/tex]
  • [tex]\huge{\orange{m\angle CBA=125\degree}}[/tex]

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