Respuesta :

anbu40

Answer:

  ∠CDH = 58°

Step-by-step explanation:

Parallel lines and angles:

  • Using Vertically opposite angle property, we need to find ∠DCF.
  • Then, using corresponding angles, we can find ∠GFH.
  • Finally using angle sum property of triangle, we can find the required angle ∠CDH.

∠ACB = ∠DCF       {Vertically opposite angles}

∠DCF =61°

BD // EI, AH is transversal,

∠GFH = ∠DCF     {Corresponding angles}

           = 61°

FG  ≅ HG

   ∠GHF = ∠GFH   {Isosceles triangle property}

   ∠GHF = 61°

In ΔCDH,

∠GHF + ∠DCH + ∠CDH = 180° {Angle sum property of triangle}

       61 + 61 + ∠CDH = 180

            122 + ∠CDH = 180

                      ∠CDH = 180 - 122

                     ∠CDH = 58°