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)
The angle measure of the obtuse angle is the sum of the measures of the two adjacent angles. So we have the equation:
(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
Substituting this value back into the equation for the first angle, we get:
x - 5 = 28 - 5 = 23
And for the second angle:
3x = 3(28) = 84
So the measures of the two unknown angles are approximately 23° and 84°.