Question

Can someone please help me find the answer to the answer?

Answer 1

According to the information given in the exercise, the triangles ABC and DEF are similar.

By definition, two triangles are similar when their corresponding angles are congruent and the ratios of the lengths of their corresponding sides are the same.

Knowing the explained above, you can set up the following proportion in order to find "x":

`\begin{gathered} (4)/(6)=(x)/(12) \\ \end{gathered}`

Now you can solve for "x":

`\begin{gathered} (12)((4)/(6))=x \\ \\ (48)/(6)=x \\ \\ x=8 \end{gathered}`

Knowing that their corresponding angles are congruent, you can determine that:

`\begin{gathered} m\angle D=m\angle A=70\degree \\ m\angle F=m\angle C=30\degree \\ m\angle E=m\angle B \end{gathered}`

By definition, the sum of the interior angles of a triangle is 180 degrees. Then, you can set up the following equation in order to find the value of "y":

`(5y-20)+70\degree+30\degree=180\degree`

Finally, you can solve for "y":

`\begin{gathered} 5y-20+70+30=180 \\ 5y-80=180 \\ 5y=180-80 \\ 5y=100 \\ \\ y=(100)/(5) \\ \\ y=20 \end{gathered}`

The answers are:

`\begin{gathered} x=8 \\ y=20 \end{gathered}`