Respuesta :

frika

Answer:

30

Step-by-step explanation:

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

  1. [tex]\angle A\cong \angle D;[/tex]
  2. [tex]\angle ACB\cong \angle DCE;[/tex]
  3. [tex]\angle B\cong \angle E.[/tex]

Consider triangle DEC. In this triangle,

  1. [tex]m\angle C=55^{\circ};[/tex]
  2. [tex]m\angle D=65^{\circ}.[/tex]

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

[tex]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}[/tex]

Hence,

[tex]m\angle B=60^{\circ}[/tex]

So,

[tex]2x=60\\ \\x=30[/tex]

ACCESS MORE
EDU ACCESS