Question 260911
Let the original angle be A, then its complement is (90-A) and its supplement is (180-A), so from the problem, you can write the proportion:
{{{(90-A)/(180-A) = 4/13}}} Cross-multiply.
{{{13(90-A) = 4(180-A)}}} Simplify and solve for A
{{{1170-13A = 720-4A}}} Add 13A to both sides.
{{{1170 = 720+9A}}} Subtract 720 from both sides.
{{{450 = 9A}}} Divide both sides by 9.
{{{50 = A}}}
The original angle is 50 degrees(?).
Check:
{{{(90-50)/(180-50) = 4/13}}}
{{{40/130 = 4/13}}}
{{{4/13 = 4/13}}} OK!