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
?(1 point)
Responses
180°
180 degrees
60°
60 degrees
30°
30 degrees
90°
90 degrees
We know that the sum of the measures of two complementary angles is 90 degrees. Therefore, since ∠A and ∠B are complementary, we can write the equation:
m∠A + m∠B = 90
Plugging in the given values, we have:
x + 2x = 90
Combining like terms, we get:
3x = 90
Dividing both sides by 3, we find:
x = 30
Since we are looking for the measure of ∠B, which is 2x, we have:
m∠B = 2x = 2(30) = 60 degrees
Therefore, the measure of ∠B is 60 degrees. The correct answer is:
60°