Since CD and DF lie on the same line, we have
[tex]CDA+ADE+FDE=180[/tex]
Clearly, CDA=90 (because ABCD is a square), and FDE=60 (because DEF is equilateral). So, the previous equation becomes
[tex]90+ADE+60=180 \iff ADE = 30[/tex]
Now, since ADE is isosceles, we have
[tex]ADE = AED[/tex]
The angle you want is the sum of AED and AEF, and they are both known by now. Sum their measures and you'll get your answer.
Answer:
m<AEF = 90°
Step-by-step explanation:
m<CDA = 90° and CDF is a straight line. So, m<ADF is also 90°.
Now we know that, equilateral triangle has each angle measure of 60°. So, m<EDF = m<DEF = 60°
m<ADE + m<EDF = 90° ---> m<ADE = 30 which is also equal to m<DAE.
So, m<AEF = m<DAE + m<DEF = 90°
