Question

In the figure, angle E measures 30°, angle F measures 57°, and angle B measures 27°. What is the measurement of angle A?

Answer 1

The sum of the measures of the interior angles of a triangle is 180. We have measures of 57, 30, and 27. We need to find the missing angle.
180 - (30 + 27 + 57) = 66

Answer 2

∠A = 66°

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°