If x:y=4:5 , then what is the value of z ?

The correct answer is Option (2) → 80

Two angles on one side of a straight line form a linear pair and add up to \(180^\circ\), and the angles opposite each other where two lines cross are vertically opposite and equal. In the figure, \(x\) and \(y\) lie side by side on one line, and \(z\) is opposite \(x\).

• Splitting in the ratio 4 : 5: \(x=4k\) and \(y=5k\)

• Linear pair: \(4k+5k=180\), so \(k=20\)

• Hence \(x=4\times20=80^\circ\) (and \(y=100^\circ\))

• Vertically opposite angles: \(z=x=80^\circ\)