We want to find the measure of ∠ BAC in the given rhombus.
Recall that in a rhombus the opposite angles are congruent. We are given the measure ∠ BCD=∠ 54. Both ∠ BAD and ∠ BCD are opposite, so they are congruent. Therefore, they have the same measure.
m∠ BAD=m∠ BCD
⇕
m∠ BAD=∠ 54
Note that in a rhombus the diagonals bisect the angles. This means that the diagonal AC bisects ∠ BAD into ∠ BAC and ∠ DAC. Therefore, the measure of ∠ BAC is half the measure of ∠ BAD.
m∠ BAC=1/2m∠ BAD ⇕
m∠ BAC=(1/2)54
Let's simplify the right-hand side of the above equation.
