An obtuse angle is formed by two adjacent angles with measures (x−5)° and (3x)°. If the resulting angle measure is 107°, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.(1 point)
Responses
A. 32° and 75°
32 degrees and 75 degrees
B. 23° and 84°
23 degrees and 84 degrees
C. 20° and 87°
20 degrees and 87 degrees
D. 28° and 79°
To find the angle measures, we need to set up an equation.
Since an obtuse angle measures greater than 90 degrees, we can set up the following equation:
(x - 5) + (3x) = 107
Combine like terms:
4x - 5 = 107
Add 5 to both sides:
4x = 112
Divide both sides by 4:
x = 28
Now we can substitute the value of x back into the original equations to find the angle measures:
(x - 5) = 28 - 5 = 23 degrees
(3x) = 3(28) = 84 degrees
Therefore, the angle measures are approximately 23 degrees and 84 degrees.
The correct answer is: B. 23° and 84°