An obtuse angle is formed by two adjacent angles with measures and . If the resulting angle
measure is , what is the angle measure of each of the two unknown angles? Round to the nearest whole
number. (1 point)
(x − 5) ° (3x) °
107°
20° and 87°
32° and 75°
28° and 79°
23° and 84°
Let's call the measure of the first angle "a" and the measure of the second angle "b".
According to the problem, we know that the angle formed by these two adjacent angles is obtuse. This means that the sum of the two angles is greater than 90 degrees but less than 180 degrees.
Since the sum of the two angles is (a + b) and it is equal to 107 degrees, we can write the equation:
a + b = 107
We are also given that the measure of the first angle is (x - 5) degrees and the measure of the second angle is 3x degrees. We can write another equation using these expressions:
x - 5 + 3x = a
4x - 5 = a
Now we can solve the system of equations to find the value of x and the angle measures.
Substituting the value of a from the second equation into the first equation, we get:
4x - 5 + b = 107
4x + b = 112
Since we don't have any information about b, we cannot solve this equation exactly. However, we can make a reasonable assumption based on the answer choices provided.
Looking at the answer choices, the only one with a sum close to 107 is "28° and 79°". So let's assume that the angle measures are 28 degrees and 79 degrees.
Substituting these values into the equations, we get:
4x - 5 = 28
4x = 33
x = 8.25
Plugging this value of x into the expression for b, we get:
b = 3(8.25) = 24.75
Rounding these values to the nearest whole number, the angle measures are approximately 28 degrees and 80 degrees.
Therefore, the correct answer is:
28° and 80°