Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.1 - Angles, Degrees, and Special Triangles - 1.1 Problem Set - Page 11: 29

Answer

$ 70^{\circ}$

Work Step by Step

In an isosceles triangle, the base angles ( angles opposite to equal sides) are also equal. Assuming that each base angle measures $ x^{\circ}$ Now all the three angles of the said triangle are $ 40^{\circ}$ , $ x^{\circ}$ and $ x^{\circ}$ We know that all the three angles of a triangle add up to $ 180^{\circ}$, Therefore $ 40^{\circ}$ + $ x^{\circ}$ + $ x^{\circ}$ = $ 180^{\circ}$ $ 40^{\circ}$ + $ 2x^{\circ}$ = $ 180^{\circ}$ $ 2x^{\circ}$ = $ 180^{\circ}$ - $ 40^{\circ}$ $ 2x^{\circ}$ = $ 140^{\circ}$ $ x^{\circ}$ = $\frac{140}{2}$ = $ 70^{\circ}$ Thus measure of each base angle is $ 70^{\circ}$
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