If an angle in standard position has its terminal side passing through the point $B(-3,4)$ in the coordinate plane, what is the measure of angle $BCD$ to the nearest degree?

• A. $155°$
• B. $140°$
• C. $25°$
• D. $53°$

Answer: (D)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is \(B(-3, 4)\).
2. Recall that the angle in standard position is measured from the positive x-axis to the terminal side. To find this angle, we first calculate the reference angle using the tangent function, since tangent relates the y-coordinate and x-coordinate of the point: \(\tan(\theta) = \frac{y}{x}\).
3. Calculate the reference angle \(\theta_r\) by taking the arctangent of the absolute values of the coordinates: \(\theta_r = \arctan\left(\frac{|4|}{|{-3}|}\right)\).
4. Determine the quadrant where the point \((-3, 4)\) lies. Since x is negative and y is positive, the point is in the second quadrant. Angles in the second quadrant are calculated as \$180^\circ - \theta_r$.
5. Finally, compute the angle \(\theta = 180^\circ - \theta_r\) to find the measure of angle \(BCD\) in standard position, then round to the nearest degree.