Question

angles 1 and 2 are complementary and congruent. what is the measure of angle 1? 30° 45° 50° 75°

Explanation:

Step1: Recall complementary - angle definition

Complementary angles add up to 90°. Let the measure of angle 1 be $x$ and the measure of angle 2 be $y$. So $x + y=90^{\circ}$.

Step2: Use congruent - angle property

Since angles 1 and 2 are congruent, $x = y$.

Step3: Substitute and solve

Substitute $y=x$ into $x + y=90^{\circ}$, we get $x+x = 90^{\circ}$, which simplifies to $2x=90^{\circ}$. Then $x=\frac{90^{\circ}}{2}=45^{\circ}$.

Answer:

B. $45^{\circ}$