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

23°
and 84°
23 degrees and 84 degrees

20°
and 87°
20 degrees and 87 degrees

32°
and 75°
32 degrees and 75 degrees

28°
and 79°
28 degrees and 79 degrees

Answer 1

To find the measures of the two angles, we start with the equation formed by their measures:

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

Combine the terms:

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

Now, we solve for \(x\):

\[ 4x = 107 + 5 \] \[ 4x = 112 \] \[ x = 28 \]

Now, we can find the measures of the two angles:

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

Second angle: \[ 3x = 3 \times 28 = 84° \]

Thus, the measures of the two angles are 23° and 84°. Therefore, the correct response is:

23° and 84°.