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 32° and 75° 32 degrees and 75 degrees 20° and 87° 20 degrees and 87 degrees 23° and 84° 23 degrees and 84 degrees 28° and 79°
We have two adjacent angles with measures $(x-5)^\circ$ and $(3x)^\circ$. The sum of these two angles is $107^\circ$. So,
$(x-5)^\circ+(3x)^\circ=107^\circ$.
Simplifying the left side of the equation gives $4x-5^\circ=107^\circ$. Adding $5^\circ$ to both sides of the equation gives $4x=112^\circ$. Finally, dividing both sides of the equation by 4 gives $x=28^\circ$.
So, the angle measures are $(x-5)^\circ=28^\circ-5^\circ=23^\circ$ and $(3x)^\circ=3\cdot28^\circ=84^\circ$.
Therefore, the angle measures of each of the two unknown angles are $\boxed{23^\circ\text{ and }84^\circ}$.