Question

I could please use some help.

Answer 1

Answer:

30

Step-by-step 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,

$2x=60\\ \\x=30$