Question

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. check answer remaining attempts 3

Explanation:

Step1: Use property of opposite - angles in parallelogram

In a parallelogram, opposite angles are equal. So, $\angle A=\angle C$ and $\angle B = \angle D$.
Set up the equation for $\angle B$ and $\angle D$: $5m=3m + 30$.

Step2: Solve the equation for $m$

Subtract $3m$ from both sides of the equation $5m=3m + 30$.
$5m-3m=3m + 30-3m$, which simplifies to $2m=30$.
Divide both sides by 2: $m=\frac{30}{2}=15$.

Step3: Set up the equation for $\angle A$ and $\angle C$

Since $\angle A=\angle C$, and $\angle C = 105^{\circ}$, we have $3n+3 = 105$.

Step4: Solve the equation for $n$

Subtract 3 from both sides of the equation $3n+3 = 105$: $3n+3 - 3=105 - 3$, which gives $3n=102$.
Divide both sides by 3: $n=\frac{102}{3}=34$.

Answer:

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