Hi there! The answer is 26° and 64°.
The sum of the complementary angles is (always) 90°. Let the smallest angle be represented by x. Then we get the following sum of angles.
[tex]x + (x + 38) = x + x + 38 = 2x + 38[/tex]
This sum equals 90°, so we get
[tex]2x + 38 = 90[/tex]
Subtract 38 from both sides.
[tex]2x = 52[/tex]
Divide both sides by 2.
[tex]x = 52 \div 2 = 26[/tex]
Now we now that the smallest angle measures 26°. The bigger angle measures x + 38, so
[tex]x + 38 = 26 + 38 = 64[/tex]
Hence, the angles measure 26° and 64°
