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°
