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If two lines intersects then vertically opposite angles are equal prove itplease step by step solution​

Answer» <html><body><p><strong>Answer:</strong></p><p><a href="https://interviewquestions.tuteehub.com/tag/according-366619" style="font-weight:bold;" target="_blank" title="Click to know more about ACCORDING">ACCORDING</a> to the problem, we need to prove that if two lines intersect each other, then the vertically opposite angles are equal.</p><p>Let us draw the two lines AB and CD intersecting at point O.</p><p></p><p>We know that the sum of angles <a href="https://interviewquestions.tuteehub.com/tag/lying-1081801" style="font-weight:bold;" target="_blank" title="Click to know more about LYING">LYING</a> on a straight line is 180∘180∘.</p><p>Let us consider the angles on the line CD. So, we get ∠COB+∠BOD=180∘∠COB+∠BOD=180∘.</p><p>⇒∠COB=180∘−∠BOD⇒∠COB=180∘−∠BOD ---(1).</p><p>Now, let us consider the angles on the line AB. So, we get ∠COB+∠AOC=180∘∠COB+∠AOC=180∘ ---(2).</p><p>Let us <a href="https://interviewquestions.tuteehub.com/tag/substitute-1231629" style="font-weight:bold;" target="_blank" title="Click to know more about SUBSTITUTE">SUBSTITUTE</a> equation (2) in equation (1).</p><p>So, we get 180∘−∠BOD+∠AOC=180∘180∘−∠BOD+∠AOC=180∘.</p><p>⇒∠AOC=180∘−180∘+∠BOD⇒∠AOC=180∘−180∘+∠BOD.</p><p>⇒∠AOC=∠BOD⇒∠AOC=∠BOD.</p><p>From the <a href="https://interviewquestions.tuteehub.com/tag/figure-987693" style="font-weight:bold;" target="_blank" title="Click to know more about FIGURE">FIGURE</a>, we can see that the angles ∠AOC∠AOC and ∠BOD∠BOD are vertically opposite angles.</p><p>So, we have proved that if two lines intersect each other, then the vertically opposite angles are equal.</p><p><strong>Step-by-step <a href="https://interviewquestions.tuteehub.com/tag/explanation-455162" style="font-weight:bold;" target="_blank" title="Click to know more about EXPLANATION">EXPLANATION</a>:</strong></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%5C%3A%20" title="\:"/></p><p></p></body></html>


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