## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 65

x = 6.667$^{\circ}$ or = 6$\frac{2}{3}$$^{\circ} Thus, \frac{450}{x} = 67.5^{\circ} and, \frac{150}{x} = 22.5^{\circ} #### Work Step by Step Given, that \frac{450}{x} and \frac{150}{x} are complementary angles. Thus, \frac{450}{x} + \frac{150}{x} = 90^{\circ} Since denominators are same (x), thus we can directly add the numerators ( 450 and 150) Thus, \frac{450}{x} + \frac{150}{x} = \frac{600}{x} Given \frac{600}{x} = 90^{\circ} , Thus x = \frac{600}{90}$$^{\circ}$ = $\frac{20}{3}$$^{\circ} = 6.667^{\circ} or = 6\frac{2}{3}$$^{\circ}$ Thus $\frac{450}{x}$ = 450 $\div$ $\frac{20}{3}$ = 450 $\times$ $\frac{3}{20}$ = 67.5$^{\circ}$ $\frac{150}{x}$ = 150 $\div$ $\frac{20}{3}$ = 150 $\times$ $\frac{3}{20}$ = 22.5$^{\circ}$

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