Answer:
35° if tangent at A
10° if tangent at D
Step-by-step explanation:
You want the measure of angle ABD between a tangent and a secant, where arc AC = 80° and arc CD = 130°.
Arcs
The two given arcs leave a remaining arc AD of 150°. In this sort of geometry, the arc nearest point B must be the smaller of the two arcs intercepted by the tangent and secant.
The description of the geometry is ambiguous, so the answers below are for the two possible situations.
Tangent at A
The arcs nearest and farthest from point B are 80° and 150°. This makes angle B have measure ...
B = (AD -AC)/2 = (150° -80°)/2 = 35°
Tangent at D
The arcs nearest and farthest from point B are 130° and 150°. This makes angle B have measure ...
B = (AD -CD)/2 = (150° -130°)/2 = 10°
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Additional comment
The external angle is half the difference of the intercepted arcs.
The two attachments show the two geometries that match the description in the problem statement.
