BC = 7.5
The diagram referred to in the question is attached below
BX = 4
BA = 5
BY = 6
Since XY is parallel to AC, the ratio of BX to BA must be equal to the ratio of BY to BC
To find BC, use the equation below:
BX / BA = BY / BC
Substitute BX = 4, BA = 5, and BY = 6 into the equation above
4 / 5 = 6 / BC
0.8 = 6 / BC
Cross multiply
0.8 BC = 6
Divide both sides by 0.8
BC = 6/0.8
BC = 7.5
The measure of BC is 7.5
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