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

Since ∠A and ∠B are complementary, their measures add up to 90° (since it is given that ∠C is a right angle).

That means,

m∠A + m∠B = 90°

x + 2x = 90°

3x = 90°

x = 30°

So, m∠B = 2x = 2(30°) = 60°. The measure of ∠B is 60°.