Question

angles 1 and 2 are complementary and congruent. what is the measure of angle 1?
$30^\circ$
$45^\circ$
$50^\circ$
$75^\circ$

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$, so $\angle 1 + \angle 2 = 90^\circ$.

Step2: Define congruent angles

Congruent angles are equal, so $\angle 1 = \angle 2$.

Step3: Substitute and solve

Substitute $\angle 2 = \angle 1$ into the first equation:
$\angle 1 + \angle 1 = 90^\circ$
$2\angle 1 = 90^\circ$
$\angle 1 = \frac{90^\circ}{2} = 45^\circ$

Answer:

45° (Option B)