Question
What is the measurement of ∠C if the image is rotated 305°
clockwise.
<C=2,2
clockwise.
<C=2,2
Answers
Answered by
GPT-4o mini
To find the new measure of angle \( C \) after a clockwise rotation of \( 305^\circ \), we start with the understanding of standard position angles measured counterclockwise from the positive x-axis.
Clockwise rotations are typically accounted for by subtracting the angle from \( 360^\circ \).
1. **Calculate the equivalent counterclockwise angle**:
\[
\text{Counterclockwise angle} = 360^\circ - 305^\circ = 55^\circ
\]
2. **Determine the measure of angle \( C \)**:
If angle \( C \) originally was positioned such that it corresponds to \( 2, 2 \) in the coordinate plane (which we interpret as an angle with a terminal side going through the point \( (2, 2) \)), we need to find how this angle is affected by the rotation.
Since you've rotated \( 305^\circ \) clockwise, you’ll actually be working with the new angle \( 55^\circ \) in the actual position.
Therefore, if you are referencing the position of an angle defined by the coordinates \( (2, 2) \) and rotating clockwise, the new measure of angle \( C \) is:
\[
\text{New } \angle C = 55^\circ
\]
Thus, the measurement of angle \( C \) after a \( 305^\circ \) clockwise rotation is **\( 55^\circ \)**.
Clockwise rotations are typically accounted for by subtracting the angle from \( 360^\circ \).
1. **Calculate the equivalent counterclockwise angle**:
\[
\text{Counterclockwise angle} = 360^\circ - 305^\circ = 55^\circ
\]
2. **Determine the measure of angle \( C \)**:
If angle \( C \) originally was positioned such that it corresponds to \( 2, 2 \) in the coordinate plane (which we interpret as an angle with a terminal side going through the point \( (2, 2) \)), we need to find how this angle is affected by the rotation.
Since you've rotated \( 305^\circ \) clockwise, you’ll actually be working with the new angle \( 55^\circ \) in the actual position.
Therefore, if you are referencing the position of an angle defined by the coordinates \( (2, 2) \) and rotating clockwise, the new measure of angle \( C \) is:
\[
\text{New } \angle C = 55^\circ
\]
Thus, the measurement of angle \( C \) after a \( 305^\circ \) clockwise rotation is **\( 55^\circ \)**.