3. Supplementary angles are angles that have a sum of $180^{\circ}$. If $\angle \mathrm{X}$ and $\angle \mathrm{Y}$ are supplementary, and $\angle \mathrm{X}$ is $32^{\circ}$ greater than $\angle \mathrm{Y}$, what are the values of $\angle \mathrm{X}$ and $\angle \mathrm{Y}$ ?

Step 1 ：Let \(\angle X\) and \(\angle Y\) be the angles. We are given that they are supplementary and \(\angle X\) is 32 degrees greater than \(\angle Y\). So we can set up a system of equations:

Step 2 ：\(\angle X + \angle Y = 180\)

Step 3 ：\(\angle X = \angle Y + 32\)

Step 4 ：Solve the system of equations:

Step 5 ：Substitute the second equation into the first equation: \((\angle Y + 32) + \angle Y = 180\)

Step 6 ：Simplify and solve for \(\angle Y\): \(2\angle Y = 148\) and \(\angle Y = 74\)

Step 7 ：Substitute the value of \(\angle Y\) back into the second equation: \(\angle X = 74 + 32\)

Step 8 ：\(\angle X = 106\)

Step 9 ：\(\boxed{\angle X = 106^\circ, \angle Y = 74^\circ}\)