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
20° and 87°
20 degrees and 87 degrees
32° and 75°
32 degrees and 75 degrees
23° and 84°
23 degrees and 84 degrees
28° and 79°
To solve this problem, we can set up an equation. We know that the sum of the two adjacent angles forms an obtuse angle, which means their measures add up to more than 90 degrees but less than 180 degrees.
The equation we can set up is:
(x-5) + (3x) = 107
Combining like terms, we have:
4x - 5 = 107
Adding 5 to both sides, we have:
4x = 112
Dividing both sides by 4, we have:
x = 28
Now we can substitute this value back into the original expressions to find the measures of the two unknown angles:
Angle 1 = (x-5)° = (28-5)° = 23°
Angle 2 = (3x)° = 3(28)° = 84°
So the angle measures of the two unknown angles are 23 degrees and 84 degrees.
Therefore, the answer is:
23 degrees and 84 degrees