If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. Therefore m ∠ABD is equal to m ∠DBC. Since m ∠ABD=55, we know that m∠DBC is also 55.
m ∠ABD = m ∠DBC ⇒ m ∠DBC = 55
Now, notice that ∠DBC, ∠ACB, and ∠CEB are three angles in a triangle. By the Angle Sum Theorem, we can conclude that their measures add to 180.
m ∠DBC + m ∠ACB + m∠CEB = 180
We already know that m ∠DBC = 55 and that m∠CEB=90, so let's substitute these two values into our equation to find m ∠ACB.
