Exercise 29 Page 486

Looking at the figure, we can identify four pairs of supplementary angles. However, only two of these pairs are written in terms of only one variable, $x$ or $y.$ We will use the first and the fourth pair to find the values of $y$ and $x,$ respectively. By definition, the measures of supplementary angles add up to $180^{\circ }.$ We will use the first pair of supplementary angles to form the equation that can be solved for $y.$ Let's do the same thing for $x.$ Having solved the equations, we can calculate the individual angles by substituting $x=18$ and $y=13$ into the given expressions.