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

28° and 79°
28 degrees and 79 degrees

23° and 84°
23 degrees and 84 degrees

32° and 75°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we need to set up an equation and solve for x.

Based on the given information, we know that the sum of the two adjacent angles is equal to 107°:

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

Combining like terms:

4x - 5 = 107

Adding 5 to both sides:

4x = 112

Dividing both sides by 4:

x = 28

Now that we have the value of x, we can substitute it back into the expressions for the unknown angles to find their measures:

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

Therefore, the two unknown angles are 23° and 84°.