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Answer:
The largest interior angle of ΔCDF is ∠F
Step-by-step explanation:
The bearings of the vertices of the triangle are given as follows;
The bearing of C from D = 056°
The bearing of F from D = 115°
The bearing of F from C = 184°
By angle addition property, we have;
The bearing of F from D = The bearing of C from D + ∠D
∴ ∠D = The bearing of F from D - The bearing of C from D
By plugging in the values, we have;
∠D = 115° - 056° = 59°
∠D in triangle ΔCDF = 59°
∠D = 59°
By alternate interior angles, we have;
The bearing of C from D = 056° = ∠BCD
Also, we have;
The bearing of F from C = ∠BCF + ∠ACB
∠ACB = 180°
∴ ∠BCF = The bearing of F from C - ∠ACB
∠BCF = 184 - 180° = 4°
∠C in ΔCDF = ∠BCD - ∠BCF
∴ ∠C = 056° - 4° = 52°
∠C = 52°
From angle sum property of ΔCDF, we have; ∠F = 180° - ∠C - ∠D
Therefore; ∠F = 180° - 52° - 59° = 69°
We have; ∠C = 52°, ∠D = 59°, ∠F = 69°, therefore;
∠F in triangle ΔCDF, has the largest interior angle.
