Question

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

Explanation:

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\). Let \(m\angle1 = x\). Since \(\angle1\) and \(\angle2\) are congruent, \(m\angle2 = x\).

Step2: Set up the equation

\(x + x = 90^\circ\) (because they are complementary). Simplify: \(2x = 90^\circ\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{90^\circ}{2}=45^\circ\).

Answer:

\(45^\circ\)