Question

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

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(\angle1+\angle2 = 90^{\circ}\)

Step2: Use the congruent property

Since \(\angle1\) and \(\angle2\) are congruent, \(\angle1=\angle2\). Let \(\angle1 = x\) and \(\angle2=x\).

Step3: Solve the equation

Substitute into the complementary - angle equation: \(x + x=90^{\circ}\), which simplifies to \(2x = 90^{\circ}\). Then \(x=\frac{90^{\circ}}{2}=45^{\circ}\)

Answer:

B. \(45^{\circ}\)