Since the parallelogram is a rhombus, each of its diagonals bisects a pair of opposite angles. We can see that the diagonal BD bisects ∠ABC into ∠ABE and ∠EBC. Since m∠ABC = 70^(∘), we can calculate the measure of ∠ABE.
m∠ABE = 70^(∘)2 ⇔ m∠ABE = 35^(∘)
Furthermore, the diagonals of a rhombus are perpendicular. Therefore, we know that ∠BEA is a right angle. This means that m∠BEA= 90^(∘).
Now, notice that ∠1, ∠ABE, and ∠BEA are three angles of a triangle. By the Interior Angles Sum Theorem, we can conclude that their measures add to 180.
m ∠1 + m ∠ABE + m∠BEA=180
We already know that m ∠ABE = 35 and m∠BEA = 90, so let's substitute these values into our equation to find m ∠1.
