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Anastasy [175]
2 years ago
13

In the diagram below Please help I’ll give brainliest

Mathematics
1 answer:
Luda [366]2 years ago
4 0

Answer:

m<GFA = 110

Step-by-step explanation:

1. ABCD - parallelogram                          Definition of a parallelogram

                                                                   (AB ll CD) (AD ll BC)

2. m<B + m<C = 180                                    Consectuive angles in a

   110 + m<C = 180                                       parallelogram are supplementary

    m<C = 70                                    

3. m<GCB = 1/2 m<C                                  Definition of angles bisector

   m<GCB = 70

4. m<B = m<D = 110                                    Opposite angles in a

                                                                    parrallelogram are congruent

5. m<CDG = 1/2 m<D                                 Defintion of an angle bisector

  m<CDG = 55

6. m<GCB+m<CDG+m<CGD=180              Sum of anlges in a triangle (ΔCDG)

  70 + 55 + m<CGD = 180

   125 + m<CGD = 180

   m<CGD = 55

7. m<CGD + m<DGF = 180                            Linear pair, supplmentary angles

  55 + m<DGF = 180

  m<DGF = 125

8. m<C = m<A = 70                                     Opposite angles in a paralellogram

                                                                     are congruent

9. m<ADG = 1/2m<D                                       Definiton of an angle bisector

  m<ADG = 55

10.m<ADG+m<DFG+m<GFA+m<A=360        Sum of angles in quadrilateral

   55 + 125 + m<GFA + 70 = 360                    DGFA

    m<GFA + 250 = 360

   m<GFA = 110

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