Given that $m\angle \mathrm{efg}=27°$ and $m\angle \mathrm{gfh}=65°$, what is $m\angle \mathrm{efh}$ in triangle $efg$?

• A. $88°$
• B. $118°$
• C. $92°$
• D. $38°$

Answer: (A)

Verified step by step guidance

1. Identify the points and angles given in the problem: \( m\angle efg = 27^\circ \) and \( m\angle gfh = 65^\circ \). Notice that these angles share vertex \( f \) and involve points \( e, g, h \).
2. Understand that \( m\angle efh \) is the angle at vertex \( f \) formed by points \( e \) and \( h \). Since \( e, f, g, h \) are points related through the triangle and angles, consider how these angles relate around point \( f \).
3. Recognize that angles \( m\angle efg \) and \( m\angle gfh \) are adjacent angles at vertex \( f \) that together form the larger angle \( m\angle efh \). This means you can find \( m\angle efh \) by adding \( m\angle efg \) and \( m\angle gfh \).
4. Write the equation for \( m\angle efh \) as the sum of the two given angles: \[ m\angle efh = m\angle efg + m\angle gfh \] which translates to \[ m\angle efh = 27^\circ + 65^\circ \]
5. Add the two angle measures to find \( m\angle efh \). This will give you the measure of the angle \( efh \) in degrees.