Supplementary angles have a total combined measure of #180^@#. Therefore, we know that the sum of the two angle measures of the described angles is #180^@#.
Since the ratio is #11:4#, we know that angle #1# has a measure of #11x^@# and angle #2# has a measure of #4x^@#. Since we know that the sum of the two angles is #180^@#, we can write an equation and solve for #x#:
#11x^@ + 4x^@ = 180^@#
#15x^@=180^@#
#x=12^@#
Now that we have solved for #x#, let's look back at what we already know. We know that the measures of the #2# angles are #11x^@# and #4x^@#. So the angle measures are:
#4x^@##=##4 * 12^@# #=# #color(red)(48^@)#
and
#11x^@ = 11*12^@ =color(red)(132^@)#.
Your answer is that the larger angle has a measure of #color(red)(132^@)#.
I hope that helps!
