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°.