∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 78° and minor arc CD = 124°, what i
s the measure of ∠ABD? A) 23° B) 39° C) 40° Eliminate D) 46°+-
2 answers:
Minor arc AD is 360° -124° -78° = 158°. Then angle ABD is
(158° -78°)/2 = 40°
The appropriate selection is
C) 40°
Answer:
40°
Step-by-step explanation:
First, find minor arc AD.
minor arc AD = 360 - 78 - 124 = 158
then,
∠ABD =
1
2
(minor arc AD - minor arc AC)
∠ABD =
1
2
(158 - 78)
∠ABD =
1
2
80
∠ABD = 40°
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