Question

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

Answer 1

Answer:

125°

Step-by-step 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)
• $\implies 110\degree+ x +x=180\degree$
• $\implies 2x =180\degree-110\degree$
• $\implies 2x =70\degree$
• $\implies x =35\degree$
• $\implies \purple{\bold{m\angle OBA =35\degree}}$
• $m\angle CBA=\red{\bold{m\angle OBC}} +\purple{\bold{m\angle OBA }}$
• $m\angle CBA=90\degree + 35\degree$
• $\huge{\orange{m\angle CBA=125\degree}}$