Question

May I please get help with a and c? I have already found my measurements but I still can’t get the others right

Answer 1

Part A:

Recall that the sum of the interior angles of a triangle is equal to 180°. Then we have the following

We can solve for ∠C, and ∠F using the information above

`\begin{gathered} \text{Solving for }m\angle C \\ m\angle A+m\angle B+m\angle C=180\degree \\ 84\degree+48\degree+m\angle C=180\degree \\ 132\degree+m\angle C=180\degree \\ m\angle C=180\degree-132\degree \\ m\angle C=48\degree \\ \\ \text{Solving for }m\angle F \\ m\angle D+m\angle E+m\angle F=180\degree \\ 84\degree+48\degree+m\angle F=180\degree \\ 132\degree+m\angle F=180\degree \\ m\angle F=180\degree-132\degree \\ m\angle F=48\degree \end{gathered}`

Part C:

`\begin{gathered} (AB)/(DE)=(9)/(6) \\ (AB)/(DE)=(3)/(2)\text{ (simplest form)} \\ \\ (BC)/(EF)=(9)/(6) \\ (BC)/(EF)=(3)/(2)\text{ (simplest form)} \\ \\ (CA)/(FD)=(12)/(8) \\ (CA)/(FD)=(3)/(2)\text{ (simplest form)} \end{gathered}`