If angle $DEF$ measures $75°$, what is the measure of angle $CFD$ if $CFD$ and $DEF$ are supplementary angles in standard position?

• A. $150°$
• B. $165°$
• C. $105°$
• D. $125°$

Answer: (A)

Verified step by step guidance

1. Recall that supplementary angles are two angles whose measures add up to 180 degrees. This means if two angles are supplementary, their sum is 180°.
2. Identify the given angle measure: angle \( \angle DEF \) measures 75°.
3. Since \( \angle CFD \) and \( \angle DEF \) are supplementary, set up the equation: \( \angle CFD + \angle DEF = 180^\circ \).
4. Substitute the known value into the equation: \( \angle CFD + 75^\circ = 180^\circ \).
5. Solve for \( \angle CFD \) by subtracting 75° from both sides: \( \angle CFD = 180^\circ - 75^\circ \).