Respuesta :

Answer:

C

Step-by-step explanation:

the sum of complementary angles = 90°, hence

x + 5 + x - 9 = 90

2x - 4 = 90 ( add 4 to both sides )

2x = 94 ( divide both sides by 2 )

x = 47

Thus ∠DFG = 47 + 5 = 52° and ∠JKL = 47 - 9 = 38°

Answer:

52° and 38°

Step-by-step explanation:

Givens

  • Angles DFG and JKL are complementary.
  • [tex]m \angle DFG=x+5[/tex] and [tex]m \angle JKL =x-9[/tex].

We know that

[tex]\angle DFG + \angle JKL = 90\°[/tex], by definition of complementary angles.

But, [tex]m \angle DFG=x+5[/tex] and [tex]m \angle JKL =x-9[/tex], by given.

Then, we replace

[tex]\angle DFG + \angle JKL = 90\°\\x+5+x-9=90\\2x=90+9-5\\x=\frac{94}{2}\\ x=47\°[/tex]

Then, we replace this value to find each angle.

[tex]m \angle DFG=x+5=47+5=52\°\\m \angle JKL =x-9=47-9=38\°[/tex]

And, [tex]52+38=90[/tex], which proves their complementary relation.

Therefore, the angles are 52° and 38°

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