An obtuse angle is formed by two adjacent angles with measures (x−5)°

Question

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

32°
and 75°
32 degrees and 75 degrees

20°
and 87°
20 degrees and 87 degrees

28°
and 79°
28 degrees and 79 degrees

23°
and 84°

Answer 1

To solve for the measures of the two adjacent angles \( (x - 5)° \) and \( (3x)° \) that together form an obtuse angle of \( 107° \), 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 we can find the measures of the two angles:

1. \( x - 5 = 28 - 5 = 23° \)
2. \( 3x = 3 \cdot 28 = 84° \)

Thus, the angle measures are:

\[ 23° \text{ and } 84° \]

The correct answer is 23° and 84°.