Question
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 23° and 84° 23 degrees and 84 degrees 32° and 75° 32 degrees and 75 degrees 28° and 79°
Answers
GPT 3.5
Let's set up an equation to solve for x, using the fact that the sum of the two adjacent angles is equal to the obtuse angle.
(x-5) + (3x) = 107
4x - 5 = 107
4x = 112
x = 28
Now we can substitute x back into the expressions for the two angles to find their values:
First angle: x - 5 = 28 - 5 = 23°
Second angle: 3x = 3(28) = 84°
Therefore, the angle measures of the two unknown angles are 23 degrees and 84 degrees. So the correct answer is:
23° and 84°
(x-5) + (3x) = 107
4x - 5 = 107
4x = 112
x = 28
Now we can substitute x back into the expressions for the two angles to find their values:
First angle: x - 5 = 28 - 5 = 23°
Second angle: 3x = 3(28) = 84°
Therefore, the angle measures of the two unknown angles are 23 degrees and 84 degrees. So the correct answer is:
23° and 84°