In the above figure, m∠A = 36° and m∠B = (2x + 10)°. If angles A and B are complementary angles, what are the value of x and the measure of angle B?
Since angles A and B are complementary angles, their measures add up to 90°. Therefore:
m∠A + m∠B = 90°
36° + (2x + 10)° = 90°
2x + 46 = 90
2x = 44
x = 22
Now we can substitute x back into the equation to find the measure of angle B:
m∠B = 2x + 10
m∠B = 2(22) + 10
m∠B = 44 + 10
m∠B = 54°
Therefore, the value of x is 22 and the measure of angle B is 54°.