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, we have ∠A + ∠B = 90°.

We are also given that m∠A = x° and m∠B = (2x)°.

Substituting the given values, we have x° + (2x)° = 90°.

Combining like terms, we get 3x° = 90°.

Dividing both sides of the equation by 3, we find that x° = 30°.

Since ∠B = 2x°, we can substitute the value of x° to find that ∠B = 2(30°) = 60°.

Therefore, the measure of ∠B is 60°.