Problem

In the diagram below, \(AC\), \(BD\), \(EJ\), \(HI\), and \(FG\) are line segments. Determine the measure of each unknown angle \(w\), \(x\), \(y\), and \(z\).

Horizontal line segment \(AC\) is above horizontal line segment \(EJ\).

Point \(B\) is on \(AC\) and a ray starting at B divides straight angle \(ABC\) into two angles: one angle measures \(60\degree\) and the other angled is labelled \(x\).

Line segment \(BD\) intersects \(EJ\) forming four quadrants around the point of intersection. The angle forming the top-left quadrant measures \(90\degree\) and the angle forming the bottom-right quadrant (or opposite quadrant) is labelled \(w\).

Line segment \(HI\) intersects \(EJ\) at a different point, forming four quadrants around this point of intersection. The angle forming the top-left quadrant measures \(90\degree\). Line segment \(FG\) also passes through this point of intersection and divides the top-right and bottom-left quadrants into two parts. In the top-right quadrant, the angle between \(EJ\) and \(FG\) measures \(40\degree\). In the bottom-left quadrant, the angle between \(EJ\) and \(FG\) (opposite the \(40\degree\) angle) is labelled \(y\), and the angle between \(FG\) and \(HI\) is labelled \(z\).

Problem of the Week Problem B Angle Adventures

Problem of the Week
Problem B
Angle Adventures