Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 1 - Section 1.4 - Angles and Their Relationships - Exercises - Page 37: 46

Answer

The difference between the measure of its supplement and the measure of its complement is $90^{\circ}$

Work Step by Step

Let $A$ be the supplement of $x$: $A = 180^{\circ}-x$ Let $B$ be the complement of $x$: $B = 90^{\circ}-x$ We can find the difference between $A$ and $B$: $A-B = (180^{\circ}-x)-(90^{\circ}-x)$ $A-B = 180^{\circ}-x-90^{\circ}+x$ $A-B = 180^{\circ}-90^{\circ}$ $A-B = 90^{\circ}$ The difference between the measure of its supplement and the measure of its complement is $90^{\circ}$
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