Answer:
- Part 2 - ∠EGF = 105°
- Part 3 - ∠D = 65
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Step-by-step explanation for Part-2:
We know that:
- ∠EFG = 32°
- ∠AEG = 137°
- ∠EFG + ∠FGE + ∠GEF = 180°
Work:
- ∠EFG + ∠FGE + ∠GEF = 180°
- 32 + ∠FGE + (180 - 137) = 180°
- => 32 + ∠FGE + 43 = 180°
- => 75 + ∠FGE = 180°
- => ∠FGE = 180 - 75
- => ∠FGE = ∠EGF = 105°
Hence, the measure of ∠EGF is 105°.
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Step-by-step explanation for Part-3:
We know that:
- CD = CA
- This triangle is an isosceles triangle.
- ∠D = ∠A
Work:
- 50 + ∠D + ∠A = 180
- => ∠D + ∠D = 130
- => 2∠D = 130
- => ∠D = 130/2
- => ∠D = 65
Hence, the measure of ∠D is 65°
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