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?
A) 30°
B) 90°
C) 180°
D) 60°
Since ∠A and ∠B are complementary, we have the equation:
∠A + ∠B = 90°.
Since ∠C is a straight line with ∠A and ∠B, we have the equation:
∠A + ∠B + ∠C = 180°.
Substituting the given values, we get:
x + 2x + 90 = 180.
Combining like terms, we get:
3x + 90 = 180.
Subtracting 90 from both sides, we get:
3x = 90.
Dividing both sides by 3, we get:
x = 30.
Thus, ∠B = 2x = 2*30 = 60°.
Therefore, the measure of ∠B is 60°, which corresponds to option D).