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 ___.

Answer 1

Answer:

52° and 38°

Step-by-step 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

$\angle DFG + \angle JKL = 90\°\\x+5+x-9=90\\2x=90+9-5\\x=\frac{94}{2}\\ x=47\°$

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°

Answer 2

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°