Question

ABCD is square and traingle DCE is an equilateral traingle inscribed in it .if EF is drawn perpendicular to BC ,find the measure of angle BEF?

Answer 1

Answer:

60°

Step-by-step explanation:

As tri. DEC is equilateral ....

so angle ECD = 60° (angles of equi. triangle)

angle ECF = angle BCD - angle ECD

angle ECF = 90-60 all side angles of square are 90°)

/_ ECF =30

angle CEF = 180 - ( 90 +30) .......(angle sum prop of triangle)

ANGLE CEF= 60

As line DEB is straight line (180°)

angle DEC + angle CEF +angle BEF = 180°( linear pair)

60 + 60 + angle BEF = 180

angle BEF= 180 - 120

angle BEF = 60