Tiana draws quadrilateral ABCD as shown, with the measures of ∠A=3n+3, ∠B=5m, ∠C=3m+30, and ∠D=105 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.
To determine when ABCD is guaranteed to be a parallelogram, we need to look at the properties of parallelograms.
In a parallelogram, opposite angles are congruent. This means that ∠A and ∠C must be congruent, and ∠B and ∠D must be congruent.
Setting up the equations, we have:
∠A = ∠C
3n + 3 = 3m + 30
∠B = ∠D
5m = 105
From the second equation, we can solve for m:
5m = 105
m = 105/5
m = 21
Substituting this value of m into the first equation, we can solve for n:
3n + 3 = 3(21) + 30
3n + 3 = 63 + 30
3n + 3 = 93
3n = 93 - 3
3n = 90
n = 90/3
n = 30
Therefore, if m = 21 and n = 30, Tiana is guaranteed that ABCD is a parallelogram.