Question

ABCD is a square Triangle DEF is equilateral Triangle ADE is isosceles AD= AE CDF is a straight line Show all your steps,calcutate the size of angle AEF

Answer 1

Answer:

90 degrees

Step-by-step explanation:

Triangle DEF is equilateral, therefore:

Angle DFE=Angle DEF =Angle EDF $=60^\circ$

ABCD is a square, therefore:

$\angle CDA =90^\circ$

In the straight line CF

$\angle CDA + \angle ADE + \angle EDF =180^\circ$

$90^\circ+ \angle ADE +60^\circ=180^\circ\\\angle ADE=180^\circ-(90^\circ +60^\circ)\\\angle ADE=30^\circ$

Recall that triangle ADE is an Isosceles triangle; therefore:

$\angle ADE = \angle AED=30^\circ$ (Base angles of an Isosceles Triangle)

We then have:

$\angle AEF=\angle AED+\angle DE.F$

$=30^\circ+60^\circ\\=90^\circ$