The flattened angle ADE is divided by the DX ray into two angles ADX and XDE.

The flattened angle ADE is divided by the DX ray into two angles ADX and XDE. Find the degree measures of these angles if the angle ADX is three times greater than the angle XDE.

The unfolded angle is 180 °.

We take the angle ∠ XDE as a unit, we get the values:

∠ ADX = 3 ∠ XDE,

It turns out the equations:

3 ∠ XDE + ∠ XDE = 180 °,

4 ∠ XDE = 180 °,

∠ XDE = 180 °: 4,

∠ XDE = 45 °,

∠ ADX = 3 * 45 °,

∠ ADX = 135 °,

∠ XDE = 45 °,

Answer: 45 °.