Solve Equations with Adjacent Angles Quick Check 5 of 55 of 5 Items 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 23° and 84° 23 degrees and 84 degrees 28° and 79° 28 degrees and 79 degrees 20° and 87° 20 degrees and 87 degrees 32° and 75°
To solve this problem, we can set up the equation (x-5) + (3x) = 107 and solve for x.
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 this value of x into the expressions for the unknown angles to find their measures.
The first angle is (x-5)°, so it is (28-5)° = 23°.
The second angle is (3x)°, so it is (3*28)° = 84°.
Therefore, the angle measures of the two unknown angles are 23° and 84°.
Round to the nearest whole number, we get 23° and 84°.
So, the correct answer is:
23 degrees and 84 degrees