Question

May please get help with a and c?I have tried multiple times to get the corrects for them but still couldn’t.

Answer 1

To answer this question, we need to remember that the sum of the internal angles of a triangle is equal to 180°. We have two triangles, and we need to find the measure for one of the angles of each of them.

Then we have:

Triangle ABC

We have that:

$m\angle A+m\angle B+m\angle C=180^{\circ}$

Then

$\begin{gathered} m\angle A=42^{\circ} \\ m\angle B=48^{\circ} \\ 42^{\circ}+48^{\circ}+m\angle C=180^{\circ} \\ 90^{\circ_{}}+m\angle C=180^{\circ} \end{gathered}$

Now, to solve the equation, we have to subtract 90° from both sides of the equation:

$\begin{gathered} 90^{\circ}-90^{\circ}+m\angle C=180^{\circ}-90^{\circ} \\ m\angle C=90^{\circ} \end{gathered}$

Therefore, m

Triangle DEF

We can proceed similarly in this case. Then we have:

$\begin{gathered} m\angle D+m\angle E+m\angle F=180^{\circ} \\ m\angle D=29^{\circ},m\angle E=47^{\circ} \\ 29^{\circ}+47^{\circ}+m\angle F=180^{\circ} \\ 76^{\circ}+m\angle F=180^{\circ} \end{gathered}$

Finally, we can subtract 76 degrees from both sides of the equation:

$\begin{gathered} 76^{\circ}-76^{\circ}+m\angle F=180^{\circ}-76^{\circ} \\ m\angle F=104^{\circ} \end{gathered}$

Therefore, the measure of the angle F is equal to 104 degrees, m.

In summary, we have that:

$\begin{gathered} m\angle C=90^{\circ} \\ m\angle F=104^{\circ} \end{gathered}$