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In a pair of supplementary angles, the greater angle exceeds the smaller by $50^\circ$. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.
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Let smaller angle be $x$ and greater angle be $y$. ATQ, $x+y=180$ ($\frac{1}{2}$ mark). Also $y=x+50$ ($\frac{1}{2}$ mark). Solving we get $x=65^\circ$ and $y=115^\circ$ ($\frac{1}{2} + \frac{1}{2}$ marks).