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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 of your steps, calculate the size of the angle AEF.

ABCD is a square Triangle DEF is equilateral Triangle ADE is Isosceles with ADAECDF is a straight lineShowing all of your steps calculate the size of the angle class=

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Look at line CDF and see how it includes all 3 shapes.

The angle of the square is 90 and the equilateral triangle is 60 because 180/3

90 + 60= 150

180 - 150 = 30

Angle ADE is 30 degrees

Since it is an isosceles triangle, the base angels are the same so angle AED is also 30 degrees

You know that DEF is equal to 60 so...

60 + 30 = 90 degrees

Hope this helps and have a nice day!

In the given diagram, the size of the angle AEF is 90°

Calculating the measure of an angle

From the question, we are to determine the size of angle AEF

From the given information,

ABCD is square

∴ <DCB = <CBA = = <BAD = <ADC = 90° (Each of the interior angles of a square)

Also,

Triangle DEF is equilateral

∴ <DEF = <EFD = <FDE = 60° (Each interior angle of an equilateral triangle)

Since CDF is a straight line, we can write that

<CDA + <ADE + <FDE = 180° (Sum of angles on a straight line)

Then,

90° + <ADE + 60° = 180°

150° + <ADE = 180°

<ADE = 180° - 150°

<ADE = 30°

Now,

<ADE = <AED (Base angles of an isosceles triangle)

∴ <AED = 30°

In the diagram,

<AEF = <AED + <DEF

∴ <AEF = 30° + 60°

<AEF = 90°

Hence, in the given diagram, the size of the angle AEF is 90°

Learn more on Calculating the measure of an angle here: https://brainly.com/question/16034543

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