Answer:
[tex]x^{\circ}=70^{\circ}[/tex]
Step-by-step explanation:
Lines MR and PQ are parallel. Continue the line MR up to the intersection with the line NQ. Denote the point of their intersection as A.
Consider triangle AMN. In this triangle,
- [tex]m\angle ANM=40^{\circ}[/tex] - given;
- [tex]m\angle NMA=180^{\circ }-150^{\circ}=30^{\circ}[/tex] - angles RMN and NMA are supplementary angles;
So, (as the sum of all interior angles add up to 180°)
[tex]m\angle NAM=180^{\circ}-40^{\circ}-30^{\circ}=110^{\circ}[/tex]
Angles NAM and MAQ are supplementary angles, then
[tex]m\angle MAQ = 180^{\circ}-110^{\circ}=70^{\circ}[/tex]
Angles MAQ and AQP are alternate interior angles, so they are congruant and
[tex]x^{\circ}=70^{\circ}[/tex]
