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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of each unknown angle, we need to set up an equation based on the given information.

Let's denote the measure of the first unknown angle as A, and the measure of the second unknown angle as B.

We know that the angle formed by the two adjacent angles is obtuse, which means it measures greater than 90 degrees but less than 180 degrees.

We can set up the following equation to represent this:

A + B = 107° (equation 1)

We also know that the measure of the first unknown angle is (x-5) degrees, and the measure of the second unknown angle is (3x) degrees.

Therefore, we can set up the following equations:

A = x - 5° (equation 2)
B = 3x° (equation 3)

Now, we can substitute equations 2 and 3 into equation 1 to eliminate A and B:

(x - 5°) + (3x°) = 107°

Simplifying the equation, we get:

4x - 5° = 107°

Adding 5 to both sides of the equation, we have:

4x = 112°

Dividing both sides of the equation by 4, we get:

x = 112° / 4

x = 28°

Now that we found the value of x, we can substitute it back into equations 2 and 3 to find the measure of each unknown angle:

A = 28° - 5° = 23°
B = 3(28°) = 84°

Therefore, the angle measures of the two unknown angles are approximately 23° and 84°, rounded to the nearest whole number.