Question

an angle measures $48^{\circ}$ less than the measure of its complementary angle. what is measure of each angle? $\square^{\circ}$ and $\square^{\circ}$

Explanation:

Step1: Define variables for angles

Let the smaller angle be $x$. The complementary angle is $x + 48^\circ$.

Step2: Use complementary angle property

Complementary angles sum to $90^\circ$.
$$x + (x + 48^\circ) = 90^\circ$$

Step3: Simplify and solve for $x$

Combine like terms, isolate $x$.
$$2x + 48^\circ = 90^\circ$$
$$2x = 90^\circ - 48^\circ = 42^\circ$$
$$x = \frac{42^\circ}{2} = 21^\circ$$

Step4: Find the second angle

Substitute $x$ into the complementary angle expression.
$$x + 48^\circ = 21^\circ + 48^\circ = 69^\circ$$

Answer:

$21^\circ$ and $69^\circ$