A) In a geometric diagram,

LA and
<B are complementary, and they form a straight line with <C. If mLA =x°,
B = (2x) °, and
<C = 90°, what is the measure of LB?

If LA and <B are complementary, it means that the sum of their measures is 90°. So, we have:

mLA + m<B = 90°

Since mLA = x° and m<B = 2x°, we can substitute these values in the equation:

x° + 2x° = 90°

Combining like terms:

3x° = 90°

Dividing both sides by 3:

x° = 30°

Now that we know the value of x, we can find the measure of <B:

m<B = 2x° = 2(30°) = 60°

Therefore, the measure of LB is 60°.