Step-by-step explanation:
You want to find the angle at the point of intersection when two secants intersect each other outside a circle.
Secant relation
The attachment shows secants AD and AE that meet at point A outside the circle. The secants intersect the circle at B and C, respectively, intercepting arcs BC and DE.
The measure of the angle at A, the point where the secants intersect each other, is half the difference of the measures of arc DE and arc BC:
∠A = (arc DE -arc BC)/2
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Additional comment
When points B and D coincide, the secant becomes a tangent. The same angle relation still holds.
When the two secants become two tangents, the measure of angle A can still be found as the difference of the intercepted arcs. In that case, since the arcs together form the whole circle, angle A is the supplement of arc BC.