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

Published by Brooks Cole

# Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 101: 27

#### Answer

$\angle$1 + $\angle$2 = $\angle$3 + $\angle$4 Hence proved

#### Work Step by Step

Sum of all angles of a quadrilateral = $360^{\circ}$ Sum of linear angles on a line = $180^{\circ}$ HENCE $\angle$SRQ + $\angle4 + \angle$QTS + $\angle$3= $360$ THUS (180- $\angle$1)+$\angle$4 + (180-$\angle$2) +$\angle$3=$360 \approx 360 + \angle$4 + $\angle$3 -$\angle$1 - $\angle$2 =$360$ since $(360-360=0)$ BY taking all the negative terms to The Right = $\angle$1$+ $$\angle2 =$$\angle$3 + $\angle$4 Hence proved

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