Respuesta :

meghna300

Answer:

A. 28°

Step-by-step explanation:

Given,

angle BED=82° , angle CBE=152°

ABEF=CBED

which means,all the corresponding sides and angles are equal of the two quadrilaterals,i.e., they are congruent to each other.

As such,angle AFE=angle EDC=98°

and , angle A=angle BCD

Now, considering the quadrilateral CBED,

angleCBE+angleBED+angleEDC+angleBCD=360°

So,98°+82°+152°+angleBCD=360°

or,angleBCD=360°-332°=28°

luisejr77

Answer: OPTION A.

Step-by-step explanation:

Since the sum of the interior angles of a quadrilateral is 360 degrees.

We can write the following expression:

[tex]m\angle C+m\angle BED+m\angle CBE+m\angle D=360\°[/tex]

We know that ABEF≅CBED. Then:

[tex]m\angle A=m\angle C\\\\m\angle F=m\angle D[/tex]

Substituting and solving for [tex]m\angle A[/tex], we get:

[tex]m\angle A+82\°+152\°+98\°=360\°\\\\m\angle A=360\°-82\°-152\°-98\°\\\\m\angle A=28\°[/tex]