Question

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

Explanation:

Step1: Recall Parallelogram Properties

In a parallelogram, opposite sides are equal, so \( BC = AD \). Thus, \( 6 - x = x + 2 \).
Solve for \( x \):
\( 6 - x = x + 2 \)
\( 6 - 2 = x + x \)
\( 4 = 2x \)
\( x = 2 \).

Step2: Find Length of \( \overline{BC} \)

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

Step3: Recall Angle Properties (Consecutive Angles)

In a parallelogram, consecutive angles are supplementary, and opposite angles are equal. So \( \angle A = \angle C \), meaning \( 100^\circ - y^\circ = 12^\circ + y^\circ \).
Solve for \( y \):
\( 100 - y = 12 + y \)
\( 100 - 12 = y + y \)
\( 88 = 2y \)
\( y = 44 \).

Step4: Find \( m\angle DAB \)

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

Answer:

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

(Matches: 56 → \( m\angle DAB \), 4 → Length of \( \overline{BC} \), 44 → Value of \( y \), 2 → Value of \( x \))