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∠BEC+∠DEC=180
∘
(complimentary angles)
130
∘
+∠DEC=180
∘
∠DEC=50
∘
In ΔDEC -
∠DEC+∠ECD+∠CDE=180
∘
∠CDE=110
∘
by theorem of circles -
∠BAC=∠CDE
∴∠BAC=110
∘
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AngleBAC=AngleBDC=75
Angles are equal in same segment of a circle
AngleAED+DEC=180
Angle sum property
138+AngleDEC=180
AngleDEC=180-138=42
In triangle EDC
AngleDEC +angleEDC+AngleDCF=180
Angle sum property
AngleDCE=180-117
=63
Angle ECD= 63
Angles are equal in same segment of a circle
AngleAED+DEC=180
Angle sum property
138+AngleDEC=180
AngleDEC=180-138=42
In triangle EDC
AngleDEC +angleEDC+AngleDCF=180
Angle sum property
AngleDCE=180-117
=63
Angle ECD= 63
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