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)

Question

32° and 75°

20° and 87°

28° and 79°

23°and 84°

Answer 1

To find the angle measures of the two adjacent angles, we start with the information given:

The two angles are (x - 5)° and (3x)°, and they form an obtuse angle measuring 107°.

We set up the equation: \[ (x - 5) + (3x) = 107 \] Combining like terms, we have: \[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \] Next, we add 5 to both sides: \[ 4x = 112 \] Then we divide both sides by 4: \[ x = 28 \]

Now we can find the measures of the two angles.

1. The measure of the first angle: \[ x - 5 = 28 - 5 = 23° \]

2. The measure of the second angle: \[ 3x = 3 \times 28 = 84° \]

Thus, the measures of the two angles are 23° and 84°.

The correct answer is: 23° and 84°.