Question

2 find the value of the variables in the parallelogram shown below. image of parallelogram with angles 3x°, (4x + 5)°, y° x = ____ y = ____ 3

Explanation:

Step1: Recall parallelogram angle properties

In a parallelogram, consecutive angles are supplementary (sum to \( 180^\circ \)) and opposite angles are equal. So \( 3x + (4x + 5) = 180 \).

Step2: Solve for \( x \)

Simplify the equation: \( 3x + 4x + 5 = 180 \) → \( 7x + 5 = 180 \). Subtract 5: \( 7x = 175 \). Divide by 7: \( x = 25 \).

Step3: Find \( 3x \) and \( y \)

Calculate \( 3x = 3(25) = 75^\circ \). Since opposite angles in a parallelogram are equal, \( y = 4x + 5 = 4(25) + 5 = 105^\circ \) (or use supplementary: \( y = 180 - 75 = 105 \)).

Answer:

\( x = 25 \), \( y = 105 \)