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

34 °

Step-by-step 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 °

  34°

Step-by-step explanation:

You know the following relationships are true:

Using the first two equations, you can write expressions for C and E, then substitute those into the last equation:

  C = 90 - A

  E = 90 - G

  (90 -A) + D + (90-G) = 180

  A = D - G . . . . . . . add A-180 to both sides

  A = 71° -37°

  A = 34°

34 °

Step-by-step 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 °

check the picture below.

recall that the sum of all interior angles in a triangle is 180°, and that a flat-line like the line C, D and E are sitting on, is always 180°.

Assuming the following is a triangle, A = 72°

All interior angles of a triangle added together will always equal 180°, so

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.