Tiana draws quadrilateral ABCD as shown, with the measures of ∠A, ∠B, ∠C, and ∠D represented. For what values of m and n is Tiana guaranteed that ABCD is a parallelogram? (1 point) If m= and n= , then Tiana is guaranteed that ABCD is a parallelogram.
The opposite angles of a parallelogram are congruent. So, Tiana is guaranteed that ABCD is a parallelogram if and only if ∠A ≅ ∠C and ∠B ≅ ∠D.
From the diagram, we have m + 75° = 105°, which implies that m = 30°.
Also, n + 75° = 105°, which implies that n = 30°.
Therefore, Tiana is guaranteed that ABCD is a parallelogram if m = 30° and n = 30°.