Two angles are supplementary if their measures add up to $180^\circ,$ a straight angle.

Only $\angle CFE$ is supplementary to $\angle BFC$ in the given diagram.

Two angles are supplementary if their measures add up to $180^\circ,$ a straight angle.

Only $\angle COD$ is supplementary to $\angle AOC$ in the given diagram.

Two angles are supplementary if their measures add up to $180^\circ,$ a straight angle.

Since $\overline{AC}$ is a segment, we have that $\angle BOA$ and $\angle BOC$ are supplementary. \[ m \angle BOA + m \angle BOC = 180^\circ \]

Therefore, the measure of $\angle BOC$ is given by \begin{align*} m\angle BOC &= 180^\circ - m\angle BOA \\[5pt] &= 180^\circ - 93^\circ \\[5pt] &= \bbox[3pt,Gainsboro]{\color{blue}87}^\circ. \end{align*}

Two angles are supplementary if their measures add up to $180^\circ,$ a straight angle.

Since $\overline{CE}$ is a segment, we have that $\angle COA$ and $\angle AOE$ are supplementary.

\[ m \angle COA + m \angle AOE = 180^\circ \]

Therefore, the measure of $\angle COA$ is given by

\begin{align*} m\angle COA &= 180^\circ - m\angle AOE \\[5pt] &= 180^\circ - 55^\circ \\[5pt] &= {125}^\circ \end{align*}

If two angles form a linear pair, the sum of their measures is equal to $180^\circ.$

So, the measure of an angle forming a linear pair with an angle of $75^\circ$ equals

\begin{align} 180^\circ - 75^\circ & = 105^\circ. \end{align}

Two angles are supplementary if their measures add up to $180^\circ.$

So, the measure of an angle that's supplementary to an angle of $(3x -15)^\circ$ must be

\begin{align*} 180^\circ - (3x-15)^\circ &=(180 - 3x + 15)^\circ \\[5pt] & = (180 +15 - 3x)^\circ \\[5pt] & = \big(\bbox[3pt,Gainsboro]{\color{blue}195-3x}\big)^\circ. \end{align*}

Since the two angles are supplementary, the sum of their measures is equal to $180^\circ.$ Therefore,

\begin{align*} (6x + 11^{\circ}) + (3x + 7^{\circ}) &= 180^{\circ} \\[5pt] 9x + 18^{\circ} &= 180^{\circ} \\[5pt] 9x&= 162^{\circ} \\[5pt] x&= \bbox[3pt,Gainsboro]{\color{blue}18}^\circ. \end{align*}

Since $\angle A$ and $\angle B$ are supplementary angles, we have \[ m \angle A + m \angle B = 180^\circ. \]

Therefore, we obtain:

\begin{align} (15x + 5^\circ) + (5x+15^\circ) & = 180^\circ \\[3pt] 20x + 20^\circ & = 180^\circ \\[3pt] 20x & = 160^\circ \\[3pt] x & = 8^\circ \end{align}