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 32° and 75° 32 degrees and 75 degrees 23° and 84°
Answers
GPT-4o mini
To find the measures of the two angles, we start by setting up the equation based on the information given. The sum of the two adjacent angles is 107°:
\[
(x - 5) + (3x) = 107
\]
Now, we can combine like terms:
\[
x - 5 + 3x = 107
\]
This simplifies to:
\[
4x - 5 = 107
\]
Next, we solve for \(x\) by adding 5 to both sides:
\[
4x = 112
\]
Now, divide both sides by 4:
\[
x = 28
\]
Now that we have the value of \(x\), we can find the measure of each angle:
1. The first angle:
\[
x - 5 = 28 - 5 = 23°
\]
2. The second angle:
\[
3x = 3 \times 28 = 84°
\]
So the measures of the two angles are 23° and 84°.
Rounding to the nearest whole number is not necessary here since both angles are already whole numbers.
Thus, the answer is:
**23° and 84°**
\[
(x - 5) + (3x) = 107
\]
Now, we can combine like terms:
\[
x - 5 + 3x = 107
\]
This simplifies to:
\[
4x - 5 = 107
\]
Next, we solve for \(x\) by adding 5 to both sides:
\[
4x = 112
\]
Now, divide both sides by 4:
\[
x = 28
\]
Now that we have the value of \(x\), we can find the measure of each angle:
1. The first angle:
\[
x - 5 = 28 - 5 = 23°
\]
2. The second angle:
\[
3x = 3 \times 28 = 84°
\]
So the measures of the two angles are 23° and 84°.
Rounding to the nearest whole number is not necessary here since both angles are already whole numbers.
Thus, the answer is:
**23° and 84°**