Answer:
50°
Explanation:
Where secants meet externally, the angle at their point of intersection is half the difference of the intercepted arcs.
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vertex angle = (1/2)(140° -40°) = 1/2(100°) = 50°
The vertex angle is 50°.
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Additional comment
This is in contrast to the formula for the angle where chords cross. That is half the sum of the intercepted arcs.