Answer:
∠A = 66°
Step-by-step explanation:
In the figure,
∠E = 30° , ∠F = 57°
In ΔEFD
Angle sum property: Sum of all three angles of a triangle is 180°
∠E + ∠F + ∠D = 180° (Angle sum property of a triangle)
30° + 57° + ∠D = 180°
∠D = 180° - 30° - 57°
∠D = 93°
In ΔABC
Exterior angle property: Sum of two opposite interior angle of a triangle is equal to exterior angle.
∠A + ∠B = ∠D (Exterior angle property of a triangle)
∠A + 27° = 93°
∠A = 93° - 27°
∠A = 66°
Hence, The measure of angle A is 66°
