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}`