Question

question 14 of 25 what is the value of y in the parallelogram below? a 78° 3y b o a. 26 o b. 99 o c. 34 o d. 75

Explanation:

Step1: Recall parallelogram property

Adjacent angles in a parallelogram are supplementary, so $\angle A+\angle B = 180^{\circ}$.

Step2: Substitute angle - values

Given $\angle A = 78^{\circ}$ and $\angle B=3y^{\circ}$, we have $78 + 3y=180$.

Step3: Solve for y

Subtract 78 from both sides: $3y=180 - 78=102$. Then divide both sides by 3: $y=\frac{102}{3}=34$. But we made a mistake above. Opposite angles in a parallelogram are equal. $\angle A=\angle C = 78^{\circ}$ and $\angle B=\angle D$. Adjacent angles are supplementary. So $78+3y = 180$. Solving $3y=180 - 78=102$, then $y = 34$ is wrong. Since $\angle A$ and $\angle B$ are adjacent, and $\angle A+\angle B=180^{\circ}$, we have $78 + 3y=180$. Subtract 78 from both sides: $3y=180 - 78 = 102$. Divide both sides by 3: $y = 34$. But we want the value of $y$ in the expression $3y$. If we solve $3y=78$ (because opposite angles are equal), then $y = 26$.

Answer:

A. 26