Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 222: 71

Answer

The measure of $\angle ABC$ in terms of $\beta$ $$\angle ABC=180^\circ-\beta$$

Work Step by Step

We know from the image that $\angle CBx=\beta$ Also, from the image, we get that $\angle ABC$ and $\angle CBx$ are supplementary angles, so they add up to 180 degrees. Therefore, $$\angle ABC+\angle CBx=180^\circ$$ $$\angle ABC+\beta=180^\circ$$ $$\angle ABC=180^\circ-\beta$$ This is the measure of $\angle ABC$ in terms of $\beta$.
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