请将图中的数学问题的详细解题步骤,录制成中文(字幕或语音的)视频---**Problem Identifier:** 例题 3
**Question Stem:**
如图, 在 △ABC 中, ∠A : ∠B = 1 : 2, CD 是 ∠ACB 的角平分线, CE 是 △ABC 的高, 求 ∠DCE 的度数.
**Translation of Question Stem:**
As shown in the figure, in △ABC, ∠A : ∠B = 1 : 2, CD is the angle bisector of ∠ACB, CE is the altitude of △ABC, find the measure of ∠DCE.
**Mathematical Formulas/Equations:**
∠A : ∠B = 1 : 2
**Chart/Diagram Description:**
* **Type:** Geometric figure - Triangle.
* **Main Elements:**
* **Shape:** Triangle ABC.
* **Points:** Vertices A, B, C. Points D and E are on the line segment AB.
* **Lines:** Line segments AC, BC, AB forming the triangle. Line segment CD drawn from C to D. Line segment CE drawn from C to E.
* **Angles:** ∠A, ∠B, ∠ACB are the interior angles of the triangle. ∠ACD and ∠BCD are the angles formed by the angle bisector CD. ∠AEC and ∠BEC are right angles (indicated by the square symbol at E). ∠DCE is the angle between CD and CE.
* **Annotations:** Points A, B, C, D, E are labeled. There is a right angle symbol at point E on the line segment AB, indicating CE ⊥ AB.
* **Relative Position and Direction:** E and D are located on the side AB. The order of points on AB from left to right appears to be A, E, D, B in the diagram, although the exact relative positions of E and D may vary depending on the specific angles. CE is shown as the altitude from C to AB. CD is shown as an interior line segment from C to AB. CD is the angle bisector of ∠ACB. CE is perpendicular to AB.