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
28° and 79°
28 degrees and 79 degrees
32° and 75°
32 degrees and 75 degrees
20° and 87°
20 degrees and 87 degrees
23° and 84°
23 degrees and 84 degrees
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To find the measure of each angle, we can set up the equation (x-5) + (3x) = 107, which represents the sum of the two angles being equal to 107 degrees.
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.
Substituting this value back into the equation for the first angle, we get (x-5) = 28-5 = 23 degrees.
And for the second angle, (3x) = 3(28) = 84 degrees.
Therefore, the angle measures are 23 degrees and 84 degrees.
Rounded to the nearest whole number, the angle measures are 23° and 84°.