Given a right triangle $△CGF$ with right angle at $G$, if $\angle EGF$ measures $35°$, what is the measure of $\angle CGF$?

• A. $35°$
• B. $55°$
• C. $90°$
• D. $45°$

Answer: (B)

Verified step by step guidance

1. Identify the given information: The triangle \( \triangle CGF \) is a right triangle with the right angle at vertex \( G \), so \( \angle CGF = 90^\circ \).
2. Note that the sum of the angles in any triangle is always \( 180^\circ \). Therefore, the sum of the two non-right angles in this triangle must be \( 90^\circ \) because \( 180^\circ - 90^\circ = 90^\circ \).
3. Recognize that the problem gives \( \angle EGF = 35^\circ \). Since \( E \) is not a vertex of the triangle \( CGF \), but the angle \( EGF \) shares vertex \( G \) and ray \( GF \), it implies that \( \angle EGF \) and \( \angle CGF \) are complementary angles around point \( G \).
4. Use the complementary angle relationship: \( \angle CGF + \angle EGF = 90^\circ \). Substitute the known value \( 35^\circ \) for \( \angle EGF \) to find \( \angle CGF \).
5. Calculate \( \angle CGF = 90^\circ - 35^\circ \) to find the measure of \( \angle CGF \), which is the angle you are asked to determine.