Question

I could please use some help.

Answer 1

30

Explanation:

Congruent triangles have congruent corresponding sides and angles. If triangles ABC and DEC are congruent, then

1. 
   `\angle A\cong \angle D;`
2. 
   `\angle ACB\cong \angle DCE;`
3. 
   `\angle B\cong \angle E.`

Consider triangle DEC. In this triangle,

1. 
   `m\angle C=55^(\circ);`
2. 
   `m\angle D=65^(\circ).`

The sum of the measures of all interior angles in triangle are always 180°, so

`m\angle C+m\angle D+m\angle E=180^(\circ)\\ \\55^(\circ)+65^(\circ)+m\angle E=180^(\circ)\\ \\m\angle E=180^(\circ)-55^(\circ)-65^(\circ)\\ \\m\angle E=60^(\circ)`

Hence,

`m\angle B=60^(\circ)`

So,

`2x=60\\ \\x=30`