Question

Consider parallelogram ABCD below.Use the information given in the figure to find x, m ZADB, and m ZA.AB.3502x6m ZADB =m ZA = 11130С

Answer 1

ABCD is a parallelogram, which means that:

-The opposite sides are parallel, so AB || DC and AD || BC

-The opposite sides are congruent, so AB=DC and AD=BC

-Opposite angles are congruent

-Adjacent angles are supplementary

The congruent sides are equal which means that:

`\begin{gathered} AD=BC \\ 2x=6 \end{gathered}`

1) From this expression, you can determine the value of x, you have to divide both sides of the equal sign by 2:

`\begin{gathered} (2x)/(2)=(6)/(2) \\ x=3 \end{gathered}`

2) The opposite angles are equal, which means that ∠C=∠A=113º

3) Lines AD and BC are parallel lines intersected by a transversal line DB, so that:

∠CBD and ∠ADB are alternate angles, which means that they are congruent, so ∠CBD=∠ADB=35º