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°
28° and 79°
23° and 84°
32° and 75°
To find the angle measures, we need to set up an equation.
The sum of the two adjacent angles is the obtuse angle, so we have:
(x - 5) + (3x) = 107
Combining like terms, we get:
4x - 5 = 107
Adding 5 to both sides, we get:
4x = 112
Dividing both sides by 4, we get:
x = 28
Now we can substitute x back into the original expression to find the angle measures:
x - 5 = 28 - 5 = 23
3x = 3(28) = 84
So the angle measures are 23° and 84°.
Therefore, the correct answer is 23° and 84°.