Question

$\angle g$ and $\angle h$ are complementary angles. the measure of $\angle g$ is $8^\circ$ less than the measure of $\angle h$. what is the measure of $\angle g$? what is the measure of $\angle h$? enter your answers in the boxes. $m\angle g = \square^\circ$ $m\angle h = \square^\circ$

Explanation:

Step1: Define variables for angles

Let $m\angle H = x$, then $m\angle G = x - 8^\circ$

Step2: Use complementary angle rule

Complementary angles sum to $90^\circ$, so:
$$x + (x - 8^\circ) = 90^\circ$$

Step3: Simplify and solve for $x$

$$2x - 8^\circ = 90^\circ$$
$$2x = 98^\circ$$
$$x = 49^\circ$$

Step4: Calculate $m\angle G$

Substitute $x=49^\circ$ into $m\angle G = x - 8^\circ$:
$$m\angle G = 49^\circ - 8^\circ = 41^\circ$$

Answer:

$m\angle G = 41^\circ$
$m\angle H = 49^\circ$