in a geometric diagram, <A and <B are complementary and they form a straight line with <C. If m<A = x degrees, m<B=(2x)degrees and m<C=90 degrees, what is the measure of <B?
Since <A and <B are complementary, their measures sum up to 90 degrees. Let's set up an equation to solve for x:
m<A + m<B = 90 degrees
Substituting the given values:
x + 2x = 90
Combining like terms:
3x = 90
Dividing both sides by 3:
x = 30
Now, we can find the measure of <B:
m<B = 2x = 2(30) = 60 degrees.
Therefore, the measure of <B is 60 degrees.