obtuse angle is formed by two angles with measures x-5 and 3x. if the resulting angle measures 107 degrees what is the measure of the two angles round to the nearest whole number

Answer 1

To find the measures of the two angles, we are given:

1. The first angle: \( x - 5 \)
2. The second angle: \( 3x \)

We know that these two angles form an obtuse angle that measures 107 degrees. Therefore, we can set up the equation:

\[ (x - 5) + (3x) = 107 \]

Now, combine like terms:

\[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \]

Next, add 5 to both sides:

\[ 4x = 112 \]

Now, divide by 4:

\[ x = 28 \]

Now that we have the value of \( x \), we can find the measures of the two angles:

1. First angle: \[ x - 5 = 28 - 5 = 23 \]

2. Second angle: \[ 3x = 3(28) = 84 \]

Thus, the measures of the two angles are approximately:

• First angle: \( 23 \) degrees
• Second angle: \( 84 \) degrees

To summarize, rounded to the nearest whole number, the measures of the two angles are 23 degrees and 84 degrees.