Question

DFG and JKL are complementary angles. M DFG = x+5 and m JKL=x-9. The measure of DFG is ___, and the measure of JKL is ___.

47, 43
47, 53
52, 38
52, 48

Answer 1

C

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 2

52° and 38°

Explanation:

Givens

• Angles DFG and JKL are complementary.
• 
  `m \angle DFG=x+5` and
  `m \angle JKL =x-9`.

We know that

`\angle DFG + \angle JKL = 90\°`, by definition of complementary angles.

But,
`m \angle DFG=x+5` and
`m \angle JKL =x-9`, by given.

Then, we replace

`\angle DFG + \angle JKL = 90\°\\x+5+x-9=90\\2x=90+9-5\\x=(94)/(2)\\ x=47\°`

Then, we replace this value to find each angle.

`m \angle DFG=x+5=47+5=52\°\\m \angle JKL =x-9=47-9=38\°`

And,
`52+38=90`, which proves their complementary relation.

Therefore, the angles are 52° and 38°