Question

Suppose EG = 3, EB = 8, AF = 7, m∠EBG = 19,
m∠EGF = 28, and m∠CAE = 51. Find each value.

Answer 1

Given : EG = 3, EB = 8, AF = 7, m∠EBG = 19,  m∠EGF = 28, and m∠CAE = 51.  

To Find :  EF  ,  AG  ,  ED  , m∠EFG  , m∠DFG  ,  

Solution:

EF is congruent to EG

EG = 3

=> EF  = 3

AE = EB  given

AE = 8

AG = AE + EG

=> AG = 8 + 3

=> AG = 11  

A F = 7                                                      

DF = EG = 3                                            

AD = A F - DF = 7 - 3 = 4  

m∠EFG = m∠EGF

=>  m∠EFG =  28°

m∠EAD = m∠EBG = 19°                    

m∠DFG + m∠EGF + m∠EAD = 180°  Sum of angles of a triangle

m∠EGF  = 28°  given

m∠DFG  + 28° + 19°  =  180°

=>  m∠DFG =  133°

Learn More:

Suppose EG = 3, EB = 8, AF = 7

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