# Chapter 2 - Section 2.5 - Convex Polygons - Exercises - Page 106: 29

∠1 + ∠2 = ∠3 + ∠4 HENCE PROVED

#### Work Step by Step

$\angle$RWV= $\angle$SWT (VERTICALLY OPPOSITE ANGLES ARE EQUAL) BY USING SUM OF ANGLES OF A TRIANGLE =$180^{\circ} \triangle$RWV = $\angle$1 + $\angle$2 + $\angle$RWV =180 ......(1) $\triangle$TWS = $\angle$3 + $\angle$4 + $\angle$SWT =180 .....(2) BY COMPARING 1 AND 2 $\angle$1 + $\angle$2 + $\angle$RWV = $\angle$3 +$\angle$4 + $\angle$SWT SINCE $\angle$RWV= $\angle$SWT $\angle$1 + $\angle$2 = $\angle$3 + $\angle$4 HENCE PROVED

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