Answer:
The value of x
[tex] x=56^{\circ}[/tex].
Step-by-step explanation:
Given
[tex]\triangle LMN\cong \triangle PQR[/tex]
[tex]\therefore \angle L=\angle P[/tex]
[tex]\angle M=\angle Q[/tex]
[tex]\angle N=\angle R[/tex]
The vertices of triangle LMN at L(-2,3),M(-1,6) and N(1,3).The vertices of triangle PQR at P(2,1),Q(3,-4) and R(5,-1).
[tex] m\angle L=72^{\circ}[/tex]
[tex] m\angle N=x^{\circ} [/tex]
[tex]m\angle Q=52^{\circ} [/tex]
We know that [tex] \angle Q= \angle M=52^{\circ}[/tex]
In triangle LMN
[tex]m\angle L+m\angle M+m\angle N=180^{\circ}[/tex]
By angle sum property of angles
72+52+x=180
124+x=180
By adding property of integers
x=180-124
By subtraction property of equality
[tex]x=56^{\circ}[/tex]
Hence, the measure of angle N=x=[tex]56^{\circ}[/tex].
