Answer:
29) EF is 3
30) AG = 11
31) AD = 4
32) m∠EFG 28°
33) m∠CAF = 32°
34) DF = 3
Step-by-step explanation:
29) EF is given as being congruent to EG, therefore, EF = EG = 3
30) AE = EB = 8 Given
AG = AE + EG Segment addition postulate
AG = AE + EG = EB + EG = 8 + 3 = 11 Transitive property
31) m∠EAD = m∠EBG = 19° Given
m∠DFG + m∠EGF + m∠EAD = 180° Sum of angles of a triangle
∴m∠DFG = 180° - (m∠EGF + m∠EAD) = 180° - (28° + 19°) = 133°
A F = 7 Given
DF = EG = 3 Given
AD = A F - DF = 7 - 3 = 4 From segment addition postulate
32) m∠EFG = m∠EGF = 28° Given
33) m∠CAE = 51° Given
m∠CAE = m∠CAF + m∠EAD Angle addition postulate
∴ 51° = m∠CAF + 19°
m∠CAF = 51° - 19° = 32° Subtraction of angles
m∠CAF = 32°
34) DF = EG = 3 Given.
