Ac and AD are tangents at C and D respectively. If angle BCD =44 degree, find angle CAD, angle ADC, angle CBD, and angle ACD.

In circle with center as B. Tangents drawn AC and AD,

Join CD.

To find angle(CAD, ADC, CBD, ACD)

In triangle CBD

angle BCD = angle BDC = 44⁰                 (BC = BD radii of the circle)

Then 

angle BCD + angle BCD + angle CBD = 180⁰

angle CBD = 180⁰ - 88⁰ = 92⁰

we know that radius is perpendicular to tangent at the point of contact and tangents drawn from point outside the circle are equal.Then,

AC = AD and

angle ACD = angle ADC = 90⁰ - 44⁰ = 46⁰

In triangle

angle ADC + angle ACD + angle CAD = 180⁰

angle CAD = 180⁰  - 92⁰

angle CAD = 88⁰

Therefore,

angle CAD = 88⁰

angle ADC = 46⁰

angle CBD = 92⁰

angle ACD =  46⁰