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 28° and 79° 28 degrees and 79 degrees 32° and 75°
Answers
Answered by
GPT 3.5
To find the angle measures, we need to change them into equations. Let's call the unknown angles angle A and angle B. Angle A measures (x-5)° and angle B measures (3x)°. Since the angles are adjacent, they add up to the resulting angle measure, which is 107°.
Therefore, we have the equation: (x-5) + (3x) = 107.
Combining like terms, we get: 4x - 5 = 107.
Adding 5 to both sides, we get: 4x = 112.
Dividing both sides by 4, we get: x = 28.
Plugging in x = 28 into the equation for angle A, we have: (28-5)° = 23°.
And plugging in x = 28 into the equation for angle B, we have: (3(28))° = 84°.
Therefore, the angle measures are 23° and 84°.
The answer is 23 degrees and 84 degrees.
Therefore, we have the equation: (x-5) + (3x) = 107.
Combining like terms, we get: 4x - 5 = 107.
Adding 5 to both sides, we get: 4x = 112.
Dividing both sides by 4, we get: x = 28.
Plugging in x = 28 into the equation for angle A, we have: (28-5)° = 23°.
And plugging in x = 28 into the equation for angle B, we have: (3(28))° = 84°.
Therefore, the angle measures are 23° and 84°.
The answer is 23 degrees and 84 degrees.