帮我解答这道题目---**Textual Information:**
In this diagram, ∠BAD and ∠CAE are right angles.
If m∠CAD = 44°, what is the measure of ∠BAE ?
Options:
A. 92°
B. 132°
C. 134°
D. 136°
**Chart/Diagram Description:**
* **Type:** Geometric figure showing angles formed by rays originating from a common vertex.
* **Main Elements:**
* **Point:** Point A is the vertex where multiple rays meet. Points B, C, D, and E are points on the rays.
* **Lines:** Rays AB, AC, AD, AE originate from A. Ray AB points left horizontally. Ray AC is above and to the left of AD. Ray AD is vertical, pointing upwards. Ray AE is above and to the right of AD. Arrows indicate the rays extend infinitely.
* **Angles:** Angles are formed between these rays.
* ∠BAD is stated to be a right angle (90°).
* ∠CAE is stated to be a right angle (90°).
* ∠CAD is labeled with a measure of 44°.
* **Labels:** Points A, B, C, D, E are labeled. The angle measure 44° is labeled for ∠CAD.
* **Relative Position and Direction:** Ray AB is horizontal to the left of A. Ray AD is vertical above A. Ray AC is between AB and AD. Ray AE is to the right of AD.
* **Coordinate Axes:** Not present.
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Let's analyze this angle problem step by step. We have point A as the vertex where multiple rays meet. We're given that angle BAD and angle CAE are both right angles, measuring 90 degrees. We also know that angle CAD measures 44 degrees. Our goal is to find the measure of angle BAE.
Now let's find angle BAC. Since angle BAD is a right angle measuring 90 degrees, and it's composed of angle BAC plus angle CAD, we can write the equation: 90 degrees equals angle BAC plus 44 degrees. Solving for angle BAC, we get 90 minus 44, which equals 46 degrees.
Next, let's find angle DAE. We know that angle CAE is a right angle measuring 90 degrees, and it's composed of angle CAD plus angle DAE. So we can write: 90 degrees equals 44 degrees plus angle DAE. Solving for angle DAE, we get 90 minus 44, which equals 46 degrees.
Finally, let's find angle BAE. We can calculate this by adding angle BAD and angle DAE: 90 degrees plus 46 degrees equals 136 degrees. We can verify this using an alternative method: angle BAC plus angle CAE equals 46 degrees plus 90 degrees, which also gives us 136 degrees. Therefore, the answer is D: 136 degrees.
Let's summarize our complete solution. We were given that angles BAD and CAE are both right angles measuring 90 degrees, and angle CAD measures 44 degrees. In step 1, we found angle BAC equals 46 degrees. In step 2, we found angle DAE also equals 46 degrees. Finally, in step 3, we calculated angle BAE by adding 90 degrees and 46 degrees to get 136 degrees. Therefore, the correct answer is D: 136 degrees.