Note: Figure not drawn to scale.
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°
x = 25, m∠B = 60°
To find the value of x and the measure of angle B, we use the fact that complementary angles add up to 90°.
From the given information, we know that angle A is 30° and angle B is (2x + 10)°.
Since angle A and angle B are complementary, we can set up the equation:
30° + (2x + 10)° = 90°
Simplifying the equation:
2x + 40° = 90°
Subtracting 40° from both sides:
2x = 50°
Dividing by 2:
x = 25°
So the value of x is 25°.
To find the measure of angle B, we substitute x = 25 into the expression for angle B:
m∠B = 2x + 10°
m∠B = 2(25) + 10°
m∠B = 50° + 10°
m∠B = 60°
Therefore, the value of x is 25 and the measure of angle B is 60°.
The correct answer is:
x = 25, m∠B = 60°