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?(2 points)
Responses
x = 55, m∠B = 60°
x = 55, m∠B = 60°
x = 70, m∠B = 150°
x = 70, m∠B = 150°
x = 25, m∠B = 50°
x = 25, m∠B = 50°
x = 25, m∠B = 60°
Based on the given information, we know that angles A and B are complementary, which means they add up to 90°.
Since m∠A = 30°, angle A measures 30°.
We also know that m∠B = (2x + 10)°.
Therefore, we can set up the following equation: 30 + (2x + 10) = 90.
Simplifying the equation, we have: 2x + 40 = 90.
Subtracting 40 from both sides, we get: 2x = 50.
Dividing both sides by 2, we find that x = 25.
Plugging this value back into the equation for m∠B, we have: m∠B = (2 * 25 + 10) = 60°.
Therefore, the correct answer is x = 25, m∠B = 60°.