Answers:
x = 41
y = 2
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AB = BC is given to us, shown by the single tick marks on those sides.
So we have an isosceles triangle
The base angles CAB and ACB are congruent
Therefore, angle ACB is also 49 degrees
Let z = measure of angle ABC
Focus on triangle ABC and add up the three angles 49, 49 and z. Set the sum equal to 180 and solve for z
49+49+z = 180
98+z = 180
98+z-98 = 180-98
z = 82
So angle ABC is 82 degrees. Cut this in half to get the value of x
x = measure of angle DBC
x = (1/2)*z
x = (1/2)*(angle ABC)
x = (1/2)*(82)
x = 41
We cut the angle in half because angle DBC and angle ABD are congruent angles (shown by the same angle marker)
Due to this fact, we can say that D is the midpoint of AC
So AD = DC leading to DC = 2
Therefore, y = 2
