Answer: The measures of the two angles are 34° and 56°.
Step-by-step explanation: Given that when angles are complementary, the sum of their measures is 90 degrees.
Two complementary angles have measures 2x - 10 degrees and 3x - 10 degrees.
We are to find the measure of each of the two angles.
According to the given information, we have
[tex](2x-10)^\circ+(3x-10)^\circ=90^\circ\\\\\Rightarrow 2x-10+3x-10=90\\\\\Rightarrow 5x-20=90\\\\\Rightarrow 5x=90+20\\\\\Rightarrow 5x=110\\\\\Rightarrow x=\dfrac{110}{5}\\\\\Rightarrow x=22.[/tex]
Therefore, the measures of the two angles are
[tex](2\times22-10)^\circ=(44-10)^\circ=34^\circ[/tex]
and
[tex](3\times22-10)^\circ=(66-10)^\circ=56^\circ.[/tex]
Thus, the measures of the two angles are 34° and 56°.
