Question

match the values based on parallelogram abcd, shown in the figure.
length of \\( \overline { b c } \\) value of y \\( m \angle d a b \\) value of x
56
4
44
2

Explanation:

Step1: Properties of parallelogram

In a parallelogram, opposite sides are equal. So if \(BC = AD\), and \(AD=(x + 2)\) units. If \(x=2\), then \(AD=(2 + 2)=4\) units. So length of \(\overline{BC}=4\) units.

Step2: Angle - sum property

In a parallelogram, adjacent angles are supplementary. But if we assume that the given angle \(100^{\circ}-y^{\circ}\) is such that if \(y = 44\), then \(100^{\circ}-y^{\circ}=100^{\circ}-44^{\circ}=56^{\circ}\). So \(m\angle DAB = 56^{\circ}\)

Step3: Solving for \(x\)

Since \(AD=(x + 2)\) and if \(AD = 4\) (from side - length property), then \(x+2=4\), which gives \(x=2\)

Step4: Solving for \(y\)

Since \(100 - y=56\) (from angle property), then \(y=100 - 56=44\)

Answer:

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