Answer:
a: 45°
Step-by-step explanation:
Since the base of the pyramid is a triangle, we can use the angle property of a triangle to solve for the unknown angle. Since all the angles in a triangle add up to 180°, we can add up our current angles and subtract that value by 180 to get the unknown angle.
Solving:
[tex]\section*{Unknown Angle:}Given the triangle \( \triangle EGF \):\begin{itemize} \item \(\angle E = 60^\circ\) \item \(\angle G = 75^\circ\) \item \(\angle F = ?\)\end{itemize}\\\\\\\ \begin{equation} \angle E + \angle G + \angle F = 180^\circ ~~(\text{Since all angles in a triangle add up to 180}^\circ\ )[/tex]
[tex]\text{Substituting the known values:}\\\\\begin{equation}60^\circ + 75^\circ + \angle F = 180^\circ \\\\ \text{Simplifying:}\\\\~\begin{equation}135^\circ + \angle F = 180^\circ \\\\ \text{Solving for \( \angle F \):}\\\\\begin{equation}\angle F = 180^\circ - 135^\circ\begin{equation}\\\\\angle F = 45^\circ[/tex]
Therefore, angle F is 45°.
