Question

If line AD is a tangent to circle B at point C, and m∠ABC = 40º, what is the measure of ∠BAC?

90º 

180º 

 50º 

 40º

Answer 1

50

Explanation:

Answer 2

We have a line tangent to the circle with center B at point C. We know that the angle formed between the tangent line at the point of intersection to the line extended from that point to the center of the circle is equal to 90°. In the problem, the 90° is for ∠BCA. We also know that the summation of all angles in a triangle is 180°. We have the solution below for the ∠BAC
180°=∠BAC + ∠BCA + ∠ABC
180°=∠BAC + 90° + 40°
∠BAC =50°
The answer is 50°.