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 28° and 79° 28 degrees and 79 degrees 20° and 87° 20 degrees and 87 degrees 32° and 75° 32 degrees and 75 degrees 23° and 84°

Answer 1

Let the measure of the first unknown angle be (x - 5)° and the measure of the second unknown angle be (3x)°. Since an obtuse angle is formed, the sum of the two angles must be greater than 180°. Therefore, we have the equation (x - 5) + (3x) > 180.
Simplifying the equation gives us 4x - 5 > 180.
Adding 5 to both sides of the equation gives us 4x > 185.
Dividing both sides of the equation by 4 gives us x > 46.25.
Since x must be an integer, the smallest possible value for x is 47.
Substituting x = 47 back into the original equations gives us (x - 5) = 42 and (3x) = 141.
Therefore, the angle measures of the two unknown angles are approximately 42° and 141°.
Rounding to the nearest whole number gives us 42° and 141°.
Therefore, the correct answer is 42° and 141°.

Answer 2

the answers are
1. 28 and 79
2. 20 and 87
3. 32 and 75
4. 23 and 84

Answer 3

Apologies for the mistake in my previous response. Let's solve the problem correctly.

The sum of the two adjacent angles is the measure of the obtuse angle, which is given as 107°. So we have the equation: (x - 5) + (3x) = 107.

Combining like terms, we get 4x - 5 = 107.

Adding 5 to both sides, we have 4x = 112.

Dividing both sides by 4, we find x = 28.

Substituting x = 28 back into the original expressions, we get the angle measures as (x - 5) = 28 - 5 = 23° and (3x) = 3(28) = 84°.

Therefore, the angle measures of the two unknown angles are 23° and 84°. Thus, the correct answer is 23° and 84°.