Question

find the value of each variable in each parallelogram.
3.
4.
5.
6.

Explanation:

Problem 3:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary, and opposite angles are equal. Here, the angle \( (2x - 1)^\circ \) should be equal to \( 75^\circ \) (opposite angles in parallelogram are equal). So we set up the equation:
\( 2x - 1 = 75 \)

Step2: Solve for \( x \)

Add 1 to both sides:
\( 2x = 75 + 1 = 76 \)
Divide both sides by 2:
\( x = \frac{76}{2} = 38 \)

Step1: Recall parallelogram side property

In a parallelogram, opposite sides are equal. The side of length 11 is opposite to the side \( y - 4 \), and the side of length 8 is opposite to its corresponding side (but here we focus on \( y \)). So we set \( y - 4 = 11 \)

Step2: Solve for \( y \)

Add 4 to both sides:
\( y = 11 + 4 = 15 \)

Step1: Recall parallelogram side properties

In a parallelogram, opposite sides are equal. So for the sides with \( a \): \( 3a + 7 = 4a \) and for sides with \( b \): \( b + 11 = 2b \)

Step2: Solve for \( a \)

From \( 3a + 7 = 4a \), subtract \( 3a \) from both sides:
\( 7 = 4a - 3a \)
\( a = 7 \)

Step3: Solve for \( b \)

From \( b + 11 = 2b \), subtract \( b \) from both sides:
\( 11 = 2b - b \)
\( b = 11 \)

Answer:

\( x = 38 \)

Problem 4: