Question

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

32°
and 75°
32 degrees and 75 degrees

28°
and 79°
28 degrees and 79 degrees

23°
and 84°

Answer 1

To solve for the measures of the two angles, we start by establishing the relationship between the two angles based on the information provided.

The given angles are:

1. \((x - 5)°\)
2. \((3x)°\)

According to the problem, the sum of these two angles is \(107°\): \[ (x - 5) + (3x) = 107 \]

Now we can simplify the equation: \[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \]

Next, we will add 5 to both sides: \[ 4x = 112 \]

Now, we divide both sides by 4: \[ x = 28 \]

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

1. The first angle: \[ x - 5 = 28 - 5 = 23° \]
2. The second angle: \[ 3x = 3 \times 28 = 84° \]

Therefore, the measures of the two angles are \(23°\) and \(84°\).

Thus, the correct response is: 23° and 84°.