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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>Step-by-step explanation:</strong></p><p>According to the problem, we need to prove that if two lines intersect each other, then the vertically opposite angles are equal.</p><p><a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> us draw the two lines AB and CD intersecting at point O.</p><p></p><p>We know that the sum of angles lying on a straight <a href="https://interviewquestions.tuteehub.com/tag/line-1074199" style="font-weight:bold;" target="_blank" title="Click to know more about LINE">LINE</a> is 180∘180∘.</p><p>Let us consider the angles on the line CD. So, we <a href="https://interviewquestions.tuteehub.com/tag/get-11812" style="font-weight:bold;" target="_blank" title="Click to know more about GET">GET</a> ∠COB+∠BOD=180∘∠COB+∠BOD=180∘.</p><p>⇒∠COB=180∘−∠BOD⇒∠COB=180∘−∠BOD ---(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>).</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 substitute <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> (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 figure, 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></body></html>


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