< ADF measures 2x degrees and < FDC measures x + 12 degrees. What is the measure

Mathematics

1 answer:

gtnhenbr [62]3 years ago

7 0

Answer:

<h2>Angle ADF is equal to 52° and angle FDC is equal to 38°.</h2>

Step-by-step explanation:

In the image attaches, you can observe that angles ADF and FDC are complementary angles, because they sum 90°.

$\angle ADF + \angle FDC = 90\°$

And we know that

$\angle ADF=2x\\\angle FDC = x+12$

Replacing these expressions, we have

$2x+x+12=90\°\\3x=90\° - 12\°\\x=\frac{78}{3}\\ x=26$

Then, we replace this value in each expression to find both angles measures.

$\angle ADF= 2(26)=52\°\\\angle FDC = 26+12=38\°$

Therefore, angle ADF is equal to 52° and angle FDC is equal to 38°.

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