The given triangle is ABC, A(-2.2), B(3,4), C(-4,7), construction) angle at the top C

First, we compute the slopes of the lines BC and AC using the formula:

m = \frac{y_2 - y_1}{x_2 - x_1}

Slope of BC:
m_{BC} = \frac{7 - 4}{-4 - 3} = -\frac{3}{7}

Slope of AC:
m_{AC}=\frac{7-2}{-4-(-2)}=-\frac{5}{2}

Now, we can find the measure of angle C using the formula:

\angle C=\tan^{-1}\left|\right.\frac{m_2 - m_1}{1 + m_1 \cdot m_2}|

Where m_1 and m_2 are the slopes of two lines that form angle C.

Angle C:
\angle C=\tan^{-1}\left|\right.\frac{-\frac{5}{2}-\left(-\frac{3}{7}\right)}{1+\left(-\frac{3}{7}\right)\left(-\frac{5}{2}\right)}|
\angle C=\tan^{-1}\left|\right.\frac{-\frac{29}{14}}{\frac{29}{14}}|
\angle C=\tan^{-1}\left|-1\right|
\angle C=\tan^{-1}\left(1)
\angle C=45^{\circ}
Answer: The measure of angle C is 45^{\circ} .