Answer:
BC = 104
Explanation:
By the SAS postulate, ΔBDA and ΔBDC are congruent, meaning that each of the corresponding sides are equal in length.
BD = BD
AD = CD
BA = BC
If we know BA = 21x - 1 and BC = 9x + 59, then we can set them equal to each other and solve for "x".
BA = BC
21x - 1 = 9x + 59
21x = 9x + 60 Added 1 to both sides
12x = 60 Subtracted 9x from both sides
x = 60/12 Divided both sides by 12
x = 5 Reduced fraction, solved for "x"
To find BC, substitute x = 5 into the equation for BC.
BC = 9x + 59
BC = 9(5) + 59 Substituted "x" for 5
BC = 45 + 59 Multiplied 9 and 5
BC = 104 Added, solved for BC
∴ BC = 104