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
23° and 84°
23 degrees and 84 degrees
20° and 87°
20 degrees and 87 degrees
28° and 79°
28 degrees and 79 degrees
32° and 75°
To find the angle measures, we can set up an equation using the given information.
According to the problem, the resulting angle measure is 107°. This means that the sum of the two adjacent angles must equal 107°.
(x-5) + (3x) = 107
Next, let's simplify the equation by combining like terms:
4x - 5 = 107
To isolate the variable, we need to get rid of the constant term (-5) by adding 5 to both sides of the equation:
4x = 112
Finally, to solve for x, we divide both sides of the equation by 4:
x = 28
Now that we have the value of x, we can substitute it back into the expressions for the two unknown angles:
Angle 1: (x - 5) = (28 - 5) = 23°
Angle 2: (3x) = (3 * 28) = 84°
So, the angle measures of the two unknown angles are 23° and 84°.