Question

match the values based on parallelogram abcd, shown in the figure.
length of \overline{bc}
value of y
m\angle dab
value of x
2
44
4
56

Explanation:

Step1: Solve for \( x \) (opposite sides of parallelogram)

In a parallelogram, opposite sides are equal. So \( AB = CD \) and \( AD = BC \). Given \( AD=(x + 2) \) and \( BC=(6 - x) \). So \( x + 2=6 - x \).

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Step2: Solve for \( y \) (opposite angles of parallelogram)

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Also, \( \angle A=(100 - y)^\circ \) and \( \angle C=(12 + y)^\circ \), and \( \angle A=\angle C \) (opposite angles of parallelogram). So \( 100 - y=12 + y \).

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Step3: Find \( m\angle DAB \)

Substitute \( y = 44 \) into \( \angle DAB=(100 - y)^\circ \). So \( m\angle DAB=100 - 44 = 56^\circ \).

Step4: Find length of \( \overline{BC} \)

Substitute \( x = 2 \) into \( BC=(6 - x) \). So \( BC=6 - 2 = 4 \) units.

Answer:

• length of \( \overline{BC} \): 4
• value of \( y \): 44
• \( m\angle DAB \): 56
• value of \( x \): 2