Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

In The Image Below The Rail Is Comprised Of Parallelograms In Parallelogram ABCD AB 183 MBCD 60 And DC 3x 5 class=

Sagot :

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:

[tex]\begin{gathered} m\angle BCD+m\angle ADC=180\degree \\ AB=DC \end{gathered}[/tex]

The question provides the following information:

[tex]\begin{gathered} AB=18.3 \\ m\angle BCD=60\degree \\ DC=3x+5 \end{gathered}[/tex]

Hence, we have:

[tex]\begin{gathered} m\angle ADC=180-m\angle BCD=180-60 \\ m\angle ADC=120\degree \end{gathered}[/tex]

and

[tex]\begin{gathered} AB=DC \\ 18.3=3x+5 \\ 3x=18.3-5=13.3 \\ x=\frac{13.3}{3} \\ x=4.43 \end{gathered}[/tex]

ANSWER

[tex]\begin{gathered} \begin{equation*} m\angle ADC=120\degree \end{equation*} \\ x=4.43 \end{gathered}[/tex]

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.