Question

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

Answer 1

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}}`