Question

If ABCD is a square and DCE is an equilateral triangle in the given figure then angle DAE is equal to?

Answer 1

Step-by-step explanation:

As ABCD is a square, all the angles of the square are 90° each. The equilateral triangle has all the angles 60°. After the lines AE and BE are drawn, the triangle id divided into 3 equal parts. Thus, the angle of the each part is 20°. As the sum of angles of the triangles is 180°, the sum of other two angles is 160°. As the new triangle is a scalene triangle, the bottom two angles are equal. Thus the angles are 80° each. One angle of a square is 90°.Therefore, angle DAE is equal to 90°-80°=10°.

Therefore, angle DAE is equal to 10°.

Answer 2

Answer:

Step-by-step explanation:Given:figure,DE=CE(triangle DEC is an equilateral triangle),DA=CB(sides of a square are equal)

To prove:angle DAE=? Solution: In square ABCD,angle A=90degree,angle B=90 degree, angle C=90 degree and angle D=90 and all sides are equal to each other.

angle DAE-angle EAB =angle CBA-angle EAB.

(angle EAB=angle EAB common and equal in both the statements.

angle DAE-angle EAB =angle CBA-angle EAB)

Therefore,angle DAE= angle CBE

OR

In triangle EDA and ECB,

ED=CE(given)

DA=CB(given)

angle D =angle C(each 60 degree)

angle EDC+CDA=ECD+DCB

Therefore,angle CDA=ECB

Therefore,triangle EDA is congruent to triangle to triangle ECB by SAS criterion of congruence

Therefore,angle DAE = angle CBE (C.P.C.T)