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

23° and 84°
23 degrees and 84 degrees

28° and 79°
28 degrees and 79 degrees

20° and 87°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the angle measures, we need to set up an equation based on the information given. Since the obtuse angle is formed by two adjacent angles, their measures add up to the obtuse angle measure of 107°.

Let's set up 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

Now we can substitute the value of x back into the expressions for the angle measures:

First angle: x - 5 = 28 - 5 = 23°
Second angle: 3x = 3(28) = 84°

Therefore, the angle measures are 23° and 84°.

The answer is: 23 degrees and 84 degrees.