Answer:
x=3
Step-by-step explanation:
Angles and Lines
We must recall:
- The sum of the internal angles of a triangle is 180°
- Two linear angles add up to 180°
The image shows a triangle and the extension of its base to form two linear angles.
Note from the triangle, angle R is what it takes to get to 180°:
[tex]m\angle R=180-25x-(57+x)[/tex]
From the line SQ, angle R what it takes to get to 180°. Thus:
[tex]m\angle R=180-45x[/tex]
Equating:
[tex]180-25x-(57+x)=180-45x[/tex]
Subtracting 180 and simplifying:
[tex]-25x-57-x=-45x[/tex]
[tex]19x=57[/tex]
Dividing by 19:
x=3
