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Answer: B) 68</h3>
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Explanation:
Segments DB and DC are the same length. This makes triangle BCD to be isosceles. Recall that the base angles of any isosceles triangle are congruent angles. The base angles are opposite the congruent sides.
So because DB = DC, this makes B = C the congruent base angles in question. Let's say they are x for now.
Also recall that for any triangle, the three angles always add to 180 degrees.
B+C+D = 180
x+x+44 = 180
2x+44 = 180
2x = 180-44
2x = 136
x = 136/2
x = 68
So angles B and C, of triangle BCD, are 68 degrees each.
This leads to angle BCD to be 68 degrees as well.
Now we'll turn to the Tangent-Chord Theorem. This says that the angle made between a chord and a tangent is the same measure as the inscribed angle that is opposite the chord.
In this case,
- AB is the tangent
- DB is the chord we want to focus on
- angle ABD is the angle between the chord and tangent
- angle BCD is the angle opposite the chord
So because angle BCD is 68 degrees, so is angle ABD.
