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Topic: point e and point d are on the extension lines of BA and CA beside △ABC, and CF and EF are equally divided into ∠ACB and ∠AED respectively. If ∠ B = 76 and D = 42, find the size of ∠ F 。

Solution: let CF and AB intersect at point g,

∠EAD = 180-∠E-∠D = 180-∠E-42 = 138-∠E

∠CAB = 180-∠C-∠B = 180-∠C-76 = 104-∠C

∠∠EAD =∠CAB (equal to the vertex angle)

∴ 138-∠E= 104-∠C = ∠ E-∠ C = 138- 104 = 34.

At delta △EFG,

∠∠EGF =∠∠CGB (equal to vertex angle)

= 180-∠B -( 1/2)∠C

= 180-76-( 1/2)∠C

= 104-( 1/2)∠C，

∴∠f= 180-( 1/2)∠e-∠egf

= 180-( 1/2)≈E-( 104-( 1/2)≈C)

= 76-( 1/2)≈E+( 1/2)≈C)

=76-( 1/2)*(∠E-∠C)

=76-( 1/2)*34

=59