Question

May I please get help with a and b? I have tried many times but still could not get the correct answerAnswering A.

Answer 1

We can look at each triangle separately.

For ΔABC, we have two internal angles:

$\begin{gathered} m\angle A=40\degree \\ m\angle B=70\degree \end{gathered}$

The sum of the internal angles of any triangle is equal to 180°, so:

$\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 40\degree+70\degree+m\angle C=180\degree \\ 110\degree+m\angle C=180\degree \\ m\angle C=180\degree-110\degree \\ m\angle C=70\degree \end{gathered}$

So, the measure of m∠C is 70°.

For ΔDEF, we have the same two internal angles:

$\begin{gathered} m\angle D=40\degree \\ m\angle E=70\degree \end{gathered}$

So, we can use the same formula of the sum of the internal angles:

$\begin{gathered} m\angle D+m\angle E+m\angle F=180\degree \\ 40\degree+70\degree+m\angle F=180\degree \\ 110\degree+m\angle F=180\degree \\ m\angle F=180\degree-110\degree \\ m\angle F=70\degree \end{gathered}$

So, the measure of m∠F is 70°.