Find the largest interior angle of the triangle given the information below.
C bears 056° from D.
F bears 115° from D
F bears 184° from C.

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.

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