Question

in the figure shown, p || q and i is the transversal. select the correct number from each drop - down menu to show the values of z and y. z = y =

Explanation:

Step1: Use vertical - angle property

Since \(y\) and \((z - 20)^{\circ}\) are vertical angles, \(y=z - 20\).

Step2: Use corresponding - angles property

Because \(p\parallel q\) and \(l\) is the transversal, \(y = z\) (corresponding angles). Substitute \(y=z - 20\) into \(y = z\) (this is wrong, actually, since \(p\parallel q\), \(z=(z - 20)+y\) is wrong. Correctly, since \(p\parallel q\), \(z=(z - 20)+y\) is wrong. Actually, because \(p\parallel q\), \(z\) and \((z - 20)\) are supplementary (same - side interior angles). So \(z+(z - 20)=180\).

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Step3: Find \(y\)

Since \(y\) and \((z - 20)\) are vertical angles, when \(z = 100\), \(y=z-20\). Substitute \(z = 100\) into \(y=z - 20\), we get \(y = 80\).

Answer:

\(z = 100\), \(y = 80\)