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: 9

Answer

$75^{\circ}, 45^{\circ}, 120^{\circ}$

Work Step by Step

1. Given 2 interior angles and 1 exterior angle of the triangle. We can use extrerior angle to find the third interior angle of the triangle. We just need to subtract the exterior angle from 180 degrees. $180^{\circ}-(9x-12)^{\circ}=-9x+168$ 2. The sum of interior angles of the triangle equal to the 180 degrees $(6x+3)^{\circ}+(4x-3)^{\circ}+(-9x+168) ^{\circ}=180^{\circ}$ 3. Solve the equation for x: $x+168=180$ $x=12^{\circ}$ 4. Then find all the angles by replacing x=12: $6(12)+3=75^{\circ}$ $4(12)-3=45^{\circ}$ $9(12)+12=120^{\circ}$
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