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

Answer

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

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.