Answer:
34 °
Explanation:
∠D = 71°
∠G = 37°
In ΔGEF
Using angle sum property of triangle : Sum of all angles of triangle is 180°
∠G+∠E+∠F = 180°
Since ΔGEF is right angled triangle at F so, ∠F = 90°
Now, 37°+∠E+90° = 180°
127°+∠E= 180°
∠E= 180°-127° =53°
Now ∠E+∠D = 53°+71° = 124°
Now using exterior angle property in ΔABC
An exterior angle of a triangle is equal to the sum of the opposite interior angles
∠E+∠D is the exterior angle of ΔABC
So, ∠A+∠B = ∠E+∠D
since ΔABC is right angled triangle at B so, ∠B = 90°
∠A+90° = 124°
∠A = 124°-90°
∠A = 34°
Hence the measurement of angle A is 34 °