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

Step-by-step explanation:

In an equilateral triangle, all angles are equal, i. e. 60°

In triangle BEC

Angle EBC = 60° , Angle BEC = 60° and Angle BCE=60°

In triangle BFE

Angle EBF = 60° (Same angle which is = to angle EBC)

Angle BFE = 90° ( EF is bisecting angle BFE and CFE perpendicularly)

We know that,

Angle BEF + Angle EBF + Angle BFE = 180°( Angle sum property)

= Angle BEF + 60° + 90° = 180°

= Angle BEF + 150° = 180°

= Angle BEF = 180° - 150°

= Angle BEF = 30°

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