Question
an obtuse angle is formed by two adjacent angles with measures(X +10) degrees and (3X) degrees if the resulting angle measure is 118° what is the angle measure of each of the two unknown angles?
Options
43 and 75
37 and 81
20 and 98
34 and 84
Options
43 and 75
37 and 81
20 and 98
34 and 84
Answers
GPT-4o mini
To solve for the measures of the two angles, we start with the given expressions for the angles: \( (X + 10) \) degrees and \( (3X) \) degrees. The sum of these two angles is given to be 118 degrees:
\[
(X + 10) + (3X) = 118
\]
Now, combine like terms:
\[
X + 10 + 3X = 118
\]
\[
4X + 10 = 118
\]
Next, subtract 10 from both sides:
\[
4X = 118 - 10
\]
\[
4X = 108
\]
Now, divide both sides by 4 to solve for \( X \):
\[
X = \frac{108}{4} = 27
\]
Now that we have the value of \( X \), we can find the measures of the two angles:
1. The first angle: \( X + 10 = 27 + 10 = 37 \) degrees.
2. The second angle: \( 3X = 3 \times 27 = 81 \) degrees.
Thus, the two angle measures are **37 degrees** and **81 degrees**.
The correct option is **37 and 81**.
\[
(X + 10) + (3X) = 118
\]
Now, combine like terms:
\[
X + 10 + 3X = 118
\]
\[
4X + 10 = 118
\]
Next, subtract 10 from both sides:
\[
4X = 118 - 10
\]
\[
4X = 108
\]
Now, divide both sides by 4 to solve for \( X \):
\[
X = \frac{108}{4} = 27
\]
Now that we have the value of \( X \), we can find the measures of the two angles:
1. The first angle: \( X + 10 = 27 + 10 = 37 \) degrees.
2. The second angle: \( 3X = 3 \times 27 = 81 \) degrees.
Thus, the two angle measures are **37 degrees** and **81 degrees**.
The correct option is **37 and 81**.