Trigonometry (10th Edition)

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

Chapter 1 - Trigonometric Functions - Section 1.2 Angle Relationships and Similar Triangles - 1.2 Exercises: 7

Answer

All angles are 60°

Work Step by Step

1. Internal angles of a triangle have a sum of 180° $ (2x-120) ^{\circ}+(x-30) ^{\circ}+( \frac{1}{2}x+15) ^{\circ}= 180 ^{\circ}$ 2. Solve the equation for x $2x+x+\frac{1}{2}x=180+120+30-15$ $3\frac{1}{2}x=315$ $x=90^{\circ}$ 3. Then find other two angles by replacing x=90 $2(90)-120=60 ^{\circ}$ $(90)-30=60 ^{\circ}$ $180-60-60=60 ^{\circ}$
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