Question

In the given figure ABCD is a parallelogram, what is the sum of the angle x,y and z​

Answer 1

Find the sum of the given angles in a parallelogram ABCD.

Explanation:

1. As we know that a parallelogram has four sides out of which two sides are parallel to each other and has equal length and other two sides are parallel and equal in length.
2. from the figure we have a parallelogram ABCD in which we have,                            $AB||CD\ and\ AB=CD\\AC||BD\ and\ AC=BD$    
3. given angles x, y and z as, ∠$BCD=x$, ∠$CBD=y$, ∠$BAC$$=z$
4. now since $AC||BD$  angles pairs BCD, CBA and CBD, BCA form corresponding pair of angles hence, we get                                                                $\angle BCD=\angle CBA=x\\\angle CBD=\angle BCA=y$      ----(a)
5. in triangle ABC in the given parallelogram from (a) we have ,                                   $\angle A=z\ \ \ \angle B=x\ \ \ \angle C=y$                                                                                            
6. hence, through sum angles of a triangle we get,                                                     $x+y+z=180$°                            ------->ANSWER  

Answer 2

Step-by-step explanation:

answer is ...............

x +y+z= 180