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 ?
90°
180°
60°
30°
Since ∠A and ∠B are complementary, we know that their measures add up to 90°. Therefore, we can write the equation:
x° + (2x)° = 90°
Combining like terms, we get:
3x° = 90°
To solve for x, we divide both sides of the equation by 3:
x = 90° / 3 = 30°
Therefore, the measure of ∠B is equal to 2x, or 2(30°), which equals 60°.
Answer: 60°