Question

Suppose EG = 3, EV = 8, A F= 7, mebg = 19, megf = 28, and mcae= 51. Find each value.

Answer 1

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.