Question

problem 21
the measure of an angle is 22 greater than its complement. find the measure of the angle.
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Explanation:

Step1: Define variables

Let the angle be $x$ and its complement be $y$. We know that $x + y=90^{\circ}$ (by the definition of complementary - angles), and $x=y + 22$.

Step2: Substitute

Substitute $x=y + 22$ into $x + y=90$. We get $(y + 22)+y=90$.

Step3: Simplify the equation

Combine like - terms: $2y+22 = 90$.

Step4: Solve for $y$

Subtract 22 from both sides: $2y=90 - 22=68$. Then divide both sides by 2: $y = 34$.

Step5: Solve for $x$

Since $x=y + 22$, substitute $y = 34$ into this equation. So $x=34 + 22=56$.

Answer:

$56$