In the above figure, m∠A = 30° 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, we have the equation m∠A + m∠B = 90°.
Substituting the given values, we have 30° + (2x + 10)° = 90°.
Combining like terms, we have 2x + 40 = 90.
Subtracting 40 from both sides, we have 2x = 50.
Dividing both sides by 2, we have x = 25.
Substituting this value back into the expression for angle B, we have (2x + 10)° = (2 * 25 + 10)° = 60°.
Therefore, the value of x is 25 and the measure of angle B is 60°.