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: 10


$20^{\circ},35^{\circ}, 125^{\circ},55^{\circ}$

Work Step by Step

1. Given 2 interior angles and 1 exterior angle of the triangle. We can use exterior angle to find the third interior angle of the triangle. We just need to subtract the exterior angle from 180 degrees. $180^{\circ}-(7-12x)^{\circ}=12x+173$ 2. The sum of interior angles of the triangle equal to the 180 degrees $(-5x)^{\circ}+(-8x+3)^{\circ}+(12x+173) ^{\circ}=180^{\circ}$ 3. Solve the equation for x: $-x+176=180$ $x=-4^{\circ}$ 4. Then find all the interior angles by replacing x=-4: $-5(-4)=20^{\circ}$ $-8(-4)+3=35^{\circ}$ $12(-4)+173=125^{\circ}$ 5. Then find the exterior angle: $7-12(-4)=55 ^{\circ}$ It is not a coincidence that the sum of 2 interior angles equal to the exterior angle.
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