Question

ABCD is a square and triangle DEF is equilateral. Triangle ADE is isosceles with AD=AE calculate size of angle AEF

Answer 1

Angle AEF is found to be 15 degrees by subtracting angle AED (60 degrees) from angle ADE (45 degrees), based on the properties of the given shapes.

Step-by-step explanation:

Given the problem, ABCD is a square and DEF is an equilateral triangle, with an isosceles triangle ADE (where AD = AE), we are seeking to find the angle AEF. Since ABCD is a square, we know that angle DAE is 45 degrees because diagonals in a square bisect the angles.

The triangle DEF being equilateral means that all its angles are 60 degrees, so we have angle AED also as 60 degrees. The isosceles triangle ADE with AD = AE implies that angles DAE and DAE are equal, and as we previously established, they must be 45 degrees. To find angle AEF, we subtract angle AED (60 degrees) from angle ADE (45 degrees), which gives us angle AEF as 15 degrees.

Answer 2

∠AEF = 90°

Step-by-step explanation:

The size of angle AEF is given below:

Given that

ABCD is Square

CDF is a straight line

∠ADF = 90°

And triangle DEF is an Equilateral Triangle

So,

∠FDE = 60°

Now

∠ADE = 90° - 60°

= 30°

AD = AE

∠AED = 30°

∠DEF = 60° because of an equilateral triangle

Now

∠AEF = ∠AED + ∠DEF

∠AEF = 30° + 60°

∠AEF = 90°