Question

In the image below, the rail is comprised of parallelograms. In parallelogram ABCD AB = 18.3, ∠=m∠BCD= 60°, and DC = 3x + 5.

Answer 1

Recall the following properties of a parallelogram:

1) Angles on the same side of the transversal are supplementary.

2) Opposite sides are equal.

Therefore, for the given parallelogram, it can be deduced that:

`\begin{gathered} m\angle BCD+m\angle ADC=180\degree \\ AB=DC \end{gathered}`

The question provides the following information:

`\begin{gathered} AB=18.3 \\ m\angle BCD=60\degree \\ DC=3x+5 \end{gathered}`

Hence, we have:

`\begin{gathered} m\angle ADC=180-m\angle BCD=180-60 \\ m\angle ADC=120\degree \end{gathered}`

and

`\begin{gathered} AB=DC \\ 18.3=3x+5 \\ 3x=18.3-5=13.3 \\ x=(13.3)/(3) \\ x=4.43 \end{gathered}`

ANSWER

`\begin{gathered} \begin{equation*} m\angle ADC=120\degree \end{equation*} \\ x=4.43 \end{gathered}`