Question

ABCD is a square Triangle DEF is equilateral Triangle ADE is Isosceles with AD=AECDF is a straight lineShowing all of your steps, calculate the size of the angle AEF.

Answer 1

The size of ∡AEF is 90 °

Explanation:

Here we have

Since ∡CDF = straight line = 180 °

∡FDE = 60 ° = Internal angle of equilateral triangle

∡CDA = 90 ° = Internal angle of a square

∡ADE + ∡CDA + ∡FDE = 180 °, Sum of angles on a straight line

Therefore ∡ADE = 180 - (∡CDA + ∡FDE) = 180 ° - 150 ° = 30 °

∡DEA = ∡ADE = 30 °

∡AEF = ∡DEA + ∡DAF (Internal angle in equilateral triangle) = 30 + 60 = 90 °

The size of ∡AEF = 90 °.