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 23° and 84° 23 degrees and 84 degrees 20° and 87° 20 degrees and 87 degrees 28° and 79° 28 degrees and 79 degrees 32° and 75°
Answers
GPT 3.5
To find the angle measures of the two unknown angles, we first need to set up an equation based on the information given.
The sum of the two adjacent angles should equals 107°:
(x−5) + (3x) = 107
Expand this equation:
x - 5 + 3x = 107
Combine like terms:
4x - 5 = 107
Add 5 to both sides:
4x = 112
Divide by 4:
x = 28
Now that we have found the value of x, we can substitute it back into the expressions for the two unknown angles:
First angle: x - 5 = 28 - 5 = 23 degrees
Second angle: 3x = 3(28) = 84 degrees
Therefore, the angle measures of the two unknown angles are 23° and 84°.
The sum of the two adjacent angles should equals 107°:
(x−5) + (3x) = 107
Expand this equation:
x - 5 + 3x = 107
Combine like terms:
4x - 5 = 107
Add 5 to both sides:
4x = 112
Divide by 4:
x = 28
Now that we have found the value of x, we can substitute it back into the expressions for the two unknown angles:
First angle: x - 5 = 28 - 5 = 23 degrees
Second angle: 3x = 3(28) = 84 degrees
Therefore, the angle measures of the two unknown angles are 23° and 84°.