To find the measurement of ∠C when the point C (which is indicated by the coordinates (2, 2)) is rotated 19° clockwise about the origin, we first need to determine the angle that point C makes with the positive x-axis.
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Calculate the initial angle of point C: We can calculate the angle using the arctangent function: \[ \theta = \tan^{-1}\left(\frac{y}{x}\right) = \tan^{-1}\left(\frac{2}{2}\right) = \tan^{-1}(1) = 45^\circ \]
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Rotate the angle 19° clockwise: Since a clockwise rotation is considered negative in standard angle measurement, we subtract 19° from the initial angle: \[ \text{New angle} = \theta - 19° = 45° - 19° = 26° \]
Thus, the measurement of ∠C after being rotated 19° clockwise is 26°.