Question

ABCD is a rectangle in which angle CFE is 144 degree and angle ABE is equal to 30 degree find measure of angle BEF​

Answer 1

Answer:

angle BEF=84°

Step-by-step explanation:

In rectangle ABCD

Angle CFE+angle EFD =180° ...........linear pair

144°+angle EFD=180°

angle EFD=180-144°

angle EFD=36°

angle ABE+angle EBF=90°

30°+angle EBF=90°

angle EBF=90°-30°

angle EBF=60°

In ∆BFE

angleEBF+angleBFE+angleBEF =180° ....angle sum property of triangle

36°+60°+angleBEF=180°

96°+angleBEF=180°

angle BEF=180°-96°

angle BEF=84°

Answer 2

Given,

In the given figure,

ABCD is a rectangle.

∠CFE= 144°

∠ABE= 30°
To find,

∠BEF=?

Solution,

We can solve this problem by following these steps.

In the given figure BEF forms a triangle.

Let's know that the sum of all angles of a triangle= 180°

We know that each of the angles of a rectangle = 90°

i.e.,

                          ∠ABF= 90°,

If,  

                         ∠ABE= 30°

Then,

                        ∠EBF = ∠ABF- ∠ABE

                                  = 90°-30°

                                  = 60°

Now,

          ∠CFE+ ∠ EFB = 180° (Because it forms a line, )

                       ∠CFE = 144°

Then,

             144°+ ∠EFB = 180°

 ∴                   ∠EFB = 180°- ∠CFE

                                = 180°- 144°

                                = 36°

∠EBF+∠BFE+∠BEF = 180°

    60°+ 36°+∠BEF = 180°

∴                    ∠BEF= 180°- (∠EBF+∠BFE)

                               = 180°- 96°

                               = 84°

(Note: (1) Each angle of a rectangle is equal to 90°.

           (2)Sum of all angles of a triangle is 180°)

Thus, Angle BEF is equal to 84°.