To find the measures of the two unknown angles, we need to solve the equation $107 = (X - 5) + (3X)$. Simplifying, we have $107 = 4X - 5$. Adding 5 to both sides gives $112 = 4X$. Dividing both sides by 4 gives $28 = X$.
Now, we can substitute this value back into the expressions for the two unknown angles. The first angle is $X - 5 = 28 - 5 = 23$. The second angle is $3X = 3(28) = 84$.
Therefore, the two unknown angles are approximately $\boxed{23}$ and $\boxed{84}$.
An obtuse angle is formed by two adjacent angles with measures X -5 and 3X if the resulting angle measures 107, what is the angle measure of each of the two unknown angles round to the nearest whole number?
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