Question

In the figure, angle D measures 71° and angle G measures 37°. What is the measurement of angle A?

Answer 1

Assuming the following is a triangle, A = 72°

All interior angles of a triangle added together will always equal 180°, so
`180 - 71 - 37 = 72`

Answer 2

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 °