Answer:
The measure of one angle is [tex]113.6^o[/tex], and the measure of the other one is [tex]66.4^o[/tex]
Step-by-step explanation:
Recall that supplementary angles are those whose addition renders [tex]180^o[/tex]
We need to find the measure of two such angles whose difference is precisely [tex]47.2^o[/tex].
Let's call such angles x and y, and consider that angle x is larger than angle y, so we can setup the following system of equations:
[tex]x+y=180^o\\x-y=47.2^o[/tex]
We can now solve this by simply combining term by term both equations, thus cancelling the term in "y", and solving first for "x":
[tex]x+y=180^o\\x-y=47.2^o\\\\2x=180^o+47.2^o\\2x=227.2^o\\x=113.6^o[/tex]
So, now we have the answer for one of the angles (x), and can use either equation from the system to find the measure of angle "y":
[tex]y=180^o-x\\y=180^o-113.6^o\\y=66.4^o[/tex]
