To find the measure of arc CBA, we can use the property of tangents and angles formed with secants in a circle.
When a tangent line (in this case, line EF) touches a circle at a point (which is point A), the angle formed between the tangent and a line drawn from that point to any point on the circle (angle CAE in this case) is equal to half the measure of the intercepted arc. Here, the intercepted arc is arc CBA.
This can be summarized by the formula:
m∠CAE = 1/2(m arc CBA)
Given that angle CAE measures 95 degrees, we can set up the equation as follows:
95 = 1/2(m arc CBA)
To find m arc CBA, we can multiply both sides of the equation by 2:
2 × 95 = m arc CBA
m arc CBA = 190 degrees
Therefore, the measure of arc CBA is 190 degrees.