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ABCD is a square

Triangle DEF is equilateral
Triangle ADE is isosceles with AD=AE
CDF is a straight line
showing all your steps, calculate the size of angles AEF

1 Answer

4 votes

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.

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