An obtuse angle is formed by two adjacent angles with measures (x-5) degree and (3x) degree. if the resulting angle is 107 degree, what is the angle measure of each of the two unknown angles? Round to the nearest whole number
A. 20 degree and 87 degree
B. 23 degree and 84 degree
C. 28 degree and 79 degree
D. 32 degree and 75 degree
Let's use the definition of an obtuse angle, which states that an angle is obtuse if its measure is greater than 90 degrees but less than 180 degrees.
The two adjacent angles are (x-5) degrees and (3x) degrees.
The sum of these two angles is obtuse, so (x-5) + (3x) > 90 and (x-5) + (3x) < 180
Expanding the equation, we get 4x - 5 > 90 and 4x - 5 < 180
Adding 5 to both sides of the inequalities, we get 4x > 95 and 4x < 185
Dividing both sides of the inequalities by 4, we get x > 23.75 and x < 46.25
Rounding x to the nearest whole number, we get x = 24
Substituting x = 24 into the equations for the two unknown angles, we get:
Angle 1: (x-5) = (24-5) = 19 degrees
Angle 2: (3x) = (3*24) = 72 degrees
Therefore, the angle measures of the two unknown angles are 19 degrees and 72 degrees.
Rounding to the nearest whole number, the answer is:
B. 23 degree and 72 degree