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 32° and 75° 32 degrees and 75 degrees 20° and 87° 20 degrees and 87 degrees 23° and 84° 23 degrees and 84 degrees 28° and 79°
Answers
GPT 3.5
To find the value of x, we need to solve the equation (x-5) + (3x) = 107.
Combining like terms, we get 4x - 5 = 107.
Adding 5 to both sides of the equation, we get 4x = 112.
Dividing both sides by 4, we get x = 28.
Now we can plug the value of x back into the expressions for the two unknown angles to find their measures.
The first angle is (x-5) = (28-5) = 23 degrees.
The second angle is (3x) = (3*28) = 84 degrees.
So the angle measures of the two unknown angles are 23° and 84°.
Combining like terms, we get 4x - 5 = 107.
Adding 5 to both sides of the equation, we get 4x = 112.
Dividing both sides by 4, we get x = 28.
Now we can plug the value of x back into the expressions for the two unknown angles to find their measures.
The first angle is (x-5) = (28-5) = 23 degrees.
The second angle is (3x) = (3*28) = 84 degrees.
So the angle measures of the two unknown angles are 23° and 84°.