Question

In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C . If m∠A=x° , m∠B=(2x)° , and m∠C=90° , what is the measure of ∠B ?

Answer 1

Because ∠A and ∠B are complementary, we have the equation ∠A + ∠B = 90°. We are given that ∠C = 90°, so ∠A + ∠B + ∠C = 180°. Since ∠A + ∠B = 90°, we have 90° + ∠C = 180°, which implies ∠C = 90°. Therefore, ∠A + ∠B + ∠C = 90° + 90° = 180°. Thus, the measure of ∠B is 2x = 90°.