Answer
The angle measures $56^\circ$ and the measure of its complementary angle is $34^\circ$.
Work Step by Step
By definition, two angles are complementary if the sum of their measurements is $90$ degrees.
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Let $x$ be the measurement of the angle.
Then its complementary angle is $90-x$.
The difference between the measures of the angle and its complementary is $22$ degrees. Thus,
$$x-(90-x)=22$$
Apply the distributive property then combine like terms:
$x-(90-x)=22$
$x-90-(-x)=22$
$x-90+x=22$
$2x-90=22$
Add $90$ to both sides then simplify:
$2x-90+90=22+90$
$2x=112$
Divide both sides by $2$:
$\dfrac{2x}{2}=\dfrac{112}{2}$
$x=56$
Therefore, the measurement of the first angle is $56$ degrees and the measure of the its complement is $(90-56)=34$ degrees.
