Question

Can someone please help me find the answer to the following?

Answer 1

We are given a tangent and a chord of a circle. The angle ABC form by the intersection of the tangent and the chord is half the arc they both intersect, therefore, we must find the major arc of the circle, we can do that with the fact that the total arc of the circle is 360, therefore:

`\begin{gathered} \text{arcAB}=360-50 \\ \text{arcAB}=310 \end{gathered}`

Therefore, the angle is:

`\begin{gathered} \angle ABC=(1)/(2)*310 \\ \angle ABC=155 \end{gathered}`

Angle ABC is 155 degrees.