Question

given ∠x and ∠y are complementary angles. the measure of ∠y is 10° more than the measure of ∠x. what is the measure of each angle? ○ m∠y = 50° and m∠x = 10° ○ m∠y = 40° and m∠x = 50° ○ m∠y = 10° and m∠x = 40° ○ m∠y = 50° and m∠x = 40°

Explanation:

Step1: Define complementary angles rule

Complementary angles sum to $90^\circ$, so:
$$m\angle X + m\angle Y = 90^\circ$$

Step2: Translate given relation

$\angle Y$ is $10^\circ$ more than $\angle X$:
$$m\angle Y = m\angle X + 10^\circ$$

Step3: Substitute and solve for $\angle X$

Substitute Step2 into Step1:
$$m\angle X + (m\angle X + 10^\circ) = 90^\circ$$
$$2m\angle X + 10^\circ = 90^\circ$$
$$2m\angle X = 80^\circ$$
$$m\angle X = 40^\circ$$

Step4: Calculate $\angle Y$

Use Step2 with $m\angle X=40^\circ$:
$$m\angle Y = 40^\circ + 10^\circ = 50^\circ$$

Answer:

$m\angle Y = 50^\circ$ and $m\angle X = 40^\circ$