Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.2 - 3 x 3 Systems of Equations - Problem Set 11.2: 24

Answer

A is 25 degrees, B is 45 degrees, and C is 110 degrees.

Work Step by Step

We are told: $ C = A + B + 40 \\ A = B - 20 $ Since it is a triangle, we know: $ A+ B+C = 180$ Plugging in $A+B=C-40$ into equation three, we find: $ 2C - 40 = 180 \\ 2C = 220 \\ C = 110$ We plug this value and equation two into equation one to find: $ 110 = B -20 + B + 40 \\ 2B = 90 \\ B = 45$ Finally, we obtain: $ A = B - 20 = 45 - 20 = 25$
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