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Problem of the Week
Problem B and Solution
Angle Adventures


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

A description of the diagram follows.


Solution 1

Since \(\angle w\) is opposite to \(90\degree\), we know \(\angle w = 90\degree\).

Since \(\angle x\) supplementary to \(60\degree\), we know that \(\angle x = 180\degree - 60\degree = 120\degree\).

Since \(\angle y\) is opposite to \(40\degree\), we know \(\angle y = 40\degree\).

We know that \(90\degree + \angle y + \angle z = 180\degree\), so we must have \(\angle y + \angle z = 90\degree\). Since \(\angle y = 40\degree\), we have \(\angle z = 50\degree\).

Solution 2

Since the diagram is drawn to scale, you may use a protractor to find the angles.