APEDIA

In right-angled triangle BDC (since BD $\perp$ AC), $\angle BDC = 90^\circ$. We are given $\angle DBC = 22^\circ$. Therefore, $\angle C = 180^\circ - 90^\circ - 22^\circ = 68^\circ$.

In triangle AEC, the exterior angle $\angle AEB$ is equal to the sum of the two opposite interior angles. Thus, $\angle AEB = \angle CAE + \angle C$.

Substituting the known values: $\angle AEB = 36^\circ + 68^\circ = 104^\circ$. Let me recheck the options and calculation.

Wait, let's re-read carefully. The question is what is $\angle AEB$. In $\triangle BDC$, $\angle C = 180 - 90 - 22 = 68^\circ$. In $\triangle AEC$, $\angle AEC = 180 - (\angle CAE + \angle C) = 180 - (36 + 68) = 180 - 104 = 76^\circ$. $\angle AEB$ and $\angle AEC$ form a linear pair on line BC. Therefore, $\angle AEB + \angle AEC = 180^\circ \Rightarrow \angle AEB = 180^\circ - 76^\circ = 104^\circ$. Wait, let me check the image. The chosen option is 4 which is 104. Let me re-verify. Yes, my calculation is 104. The marked correct option in image is 2. Let's re-read the solution. Ah, there might be a typo in my manual calculation or the key. Let's re-read the options. Option 2 is 102, option 4 is 104. Wait, let me re-calculate $180 - (36+68) = 180 - 104 = 76$. Then $180 - 76 = 104$. The answer should be 104. Let me check the provided correct option again. Oh, it says 'Ans X 1. 103, X 2. 102, X 3. 101, tick 4. 104'. Ah, my mistake in reading the user provided text. The correct option is 4 (104). Let me re-read the user text: '☑ ☑ 1. 103° 2. 102° X3. 101 ☑ 4.104'. Wait, the checkmarks are confusing. Let me look at the image directly if possible. No, only text. Let's assume my mathematical derivation of 104 is correct based on the text. The text says 'Ans ... ☑ 4.104'. Okay, 104 is the correct answer. The user provided text has a typo, let me assume 104 is option D.

By applying the properties of triangles and exterior angles, $\angle AEB$ is calculated to be 104°.