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

32° and 75°
32 degrees and 75 degrees

28° and 79°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we need to set up an equation using the information given. Let's call the measure of the first angle (x-5)° and the measure of the second angle (3x)°.

According to the problem, an obtuse angle is formed when these two angles are added together and the result is 107°. Therefore, we can set up the equation:

(x-5) + (3x) = 107

Simplifying, we have:

4x - 5 = 107

Adding 5 to both sides:

4x = 112

Dividing both sides by 4:

x = 28

Now that we know the value of x, we can substitute it back into the equations for the two unknown angles:

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

Therefore, the angle measures of the two unknown angles are approximately 23° and 84°.