## Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole

# Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 101: 30

#### Answer

to proof - ∠B + ∠D = 180 Hence Proved

#### Work Step by Step

Sum of all the angles of a quadrilateral = 360 BA $\bot$AD AND BC $\bot$DC $\angle$A = $\angle$C =90 *....(1) $\angle$BAD +$\angle$ADC+$\angle$DCB+$\angle$CBA =360 $\angle$A +$\angle$B+$\angle$C+$\angle$D =360 90 + $\angle$B + 90 + $\angle$D = 360 ...USING (1) $\angle$B + $\angle$D = 360- 180 $\angle$B + $\angle$D = 180 Hence proved

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