Question

tiana draws quadrilateral (abcd) as shown, with the measures of (angle a,angle b,angle c,) and (angle d) represented. for what values of (m) and (n) is tiana guaranteed that (abcd) is a parallelogram? (2 points) if (m=square) and (n = square), then tiana is guaranteed that (abcd) is a parallelogram

Explanation:

Step1: Use property of consecutive angles in parallelogram

In a parallelogram, consecutive angles are supplementary. So, for \(\angle B\) and \(\angle C\), we have \(5m + 105=180\).

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Step2: Use property of opposite angles in parallelogram

In a parallelogram, opposite angles are equal. So, \(\angle A=\angle C\) and \(\angle B=\angle D\). Since \(m = 15\), \(\angle D=(3m + 30)=(3\times15+30)=75^{\circ}\). Also, \(\angle A=\angle C = 105^{\circ}\).
Set \(3n+3=105\)

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Answer:

If \(m = 15\) and \(n=34\), then Tiana is guaranteed that \(ABCD\) is a parallelogram.