Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 66

Answer

x = 2$^{\circ}$ So angles are: $\frac{80}{x}$ = $\frac{80}{2}$ = 40$^{\circ}$ $\frac{100}{x}$ = $\frac{100}{2}$ = 50$^{\circ}$

Work Step by Step

Given, that $\frac{80}{x}$ and $\frac{100}{x}$ are complementary angles. Thus, $\frac{80}{x}$ + $\frac{100}{x}$ = 90$^{\circ}$ Since denominators are same (x), thus we can directly add the numerators ( 80 and 100) Thus, $\frac{80}{x}$ + $\frac{100}{x}$ = $\frac{180}{x}$ Since $\frac{180}{x}$ = 90$^{\circ}$ thus x = $\frac{180}{90}$$^{\circ}$ = 2$^{\circ}$ So angles are: $\frac{80}{x}$ = $\frac{80}{2}$ = 40$^{\circ}$ $\frac{100}{x}$ = $\frac{100}{2}$ = 50$^{\circ}$
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