Answer:
The size of angle AEF is 15 degrees
Explanation:
To calculate the size of angle AEF, we'll follow these steps:
Step 1: Identify the relevant triangles and angles:
From the given information, we have:
Square ABCD (with all angles 90 degrees)
Equilateral triangle DEF (all angles are 60 degrees)
Isosceles triangle ADE (AD = AE)
Step 2: Determine the relationships between angles:
In triangle ADE, since AD = AE (isosceles triangle), angle ADE = angle AED.
Step 3: Determine the angles in triangle DEF:
In an equilateral triangle, all angles are equal, so each angle in DEF is 60 degrees.
Step 4: Analyze the diagram:
Considering the information given, we can determine the following:
Angle DAE = 90 degrees - angle ADE = 90 degrees - angle AED
Angle DAE + angle ADE + angle AED = 180 degrees (sum of angles in triangle ADE)
Step 5: Calculate the size of angle AED:
From step 4, we have angle DAE + angle ADE + angle AED = 180 degrees. Since angle DAE = 90 degrees, we can substitute the values:
90 degrees + angle AED + angle AED = 180 degrees
Combining like terms:
90 degrees + 2 * angle AED = 180 degrees
Subtracting 90 degrees from both sides:
2 * angle AED = 90 degrees
Dividing both sides by 2:
angle AED = 45 degrees
Step 6: Calculate the size of angle AEF:
In triangle DEF, angle DEF = angle DFE = 60 degrees (as it's an equilateral triangle).
To find angle AEF, we can subtract angle AED from angle DEF:
angle AEF = angle DEF - angle AED = 60 degrees - 45 degrees
Calculating:
angle AEF = 15 degrees
Therefore, the size of angle AEF is 15 degrees.