I need the answers for both a and b so thats why 61 points are up for grab

Step-by-step explanation:

From the picture attached,

a). Triangle in the figure is ΔBCF

b). Since, and are the parallel lines and m is a transversal line,

   m∠FBC = m∠BFG [Alternate interior angles]

   Since,   and are the parallel lines and n is a transversal line,

   m∠BCF = m∠CFE [Alternate interior angles]

   By triangle sum theorem in ΔBCF

   m∠FBC + m∠BCF + m∠BFC = 180°

   From the properties given above,

   m∠BFG + m∠CFE + m∠BFC = 180°

   m∠GFE = 180°

Therefore, angle GFE is the straight angle that will be useful in proving that the sum of the measures of the interior angles of the triangle is 180°.