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in the given figure, m parallel n and angle 1 and angle 2 are in the ratio 4:5 Determine all the angles.​

Answer» <html><body><h2><u>Answer</u> :-</h2><p>The angles are <strong>∠1</strong><strong> </strong><strong>=</strong><strong> </strong><strong>8</strong><strong>0</strong><strong>°</strong>, <strong>∠</strong><strong>2</strong><strong> </strong><strong>=</strong><strong> </strong><strong>100°</strong>,</p><p><strong>∠</strong><strong>3</strong><strong> </strong><strong>=</strong><strong> </strong><strong>8</strong><strong>0</strong><strong>°</strong>,<strong> </strong><strong>∠</strong><strong>4</strong><strong> </strong><strong>=</strong><strong> </strong><strong>100°</strong>, <strong>∠</strong><strong>5</strong><strong> </strong><strong>=</strong><strong> </strong><strong>8</strong><strong>0</strong><strong>°</strong>,</p><p><strong>∠</strong><strong>6</strong><strong> </strong><strong>=</strong><strong> </strong><strong>100°</strong>, <strong>∠</strong><strong>7</strong><strong> </strong><strong>=</strong><strong> </strong><strong>8</strong><strong>0</strong><strong>°</strong><strong> </strong>and<strong> </strong><strong>∠</strong><strong>8</strong><strong> </strong><strong>=</strong><strong> </strong><strong>100°</strong>.</p><p></p><h3>Step-by-step explanation</h3><p><strong>To </strong><strong><a href="https://interviewquestions.tuteehub.com/tag/find-11616" style="font-weight:bold;" target="_blank" title="Click to know more about FIND">FIND</a></strong><strong> </strong><strong>:</strong><strong>-</strong></p><ul><li>All the angles.</li></ul><p>[∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8]</p><p></p><p>★ <strong>Solution</strong></p><p>Given that,</p><ul><li>∠1 and ∠2 are in the ratio of 4:5.</li><li>m || n</li></ul><p></p><p><strong>Assumption</strong></p><p>Let us assume the given ratio angles as <strong>4</strong><strong>x</strong><strong> </strong>and <strong>5</strong><strong>x</strong>.</p><p><u>Therefore</u>,</p><h3>4x + 5x = 180°</h3><p></p><p><strong>⇒</strong> 4x + 5x = 180</p><p><strong>⇒</strong><strong> </strong>9x = 180</p><p><strong>⇒</strong> x = 180/9</p><p><strong>⇒</strong><strong> </strong>x = 20</p><p></p><p>The value of x is 20. Hence, <u>The angles are</u> :-</p><p><strong>⇒</strong> ∠1 = 4x = 4*20 = <strong>8</strong><strong>0</strong><strong>°</strong></p><p><strong>⇒</strong> ∠2 = 5x = 5*20 = <strong>100°</strong> </p><p><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u> </p><p>Now, The angles are :-</p><p>As given <strong>m </strong><strong>|</strong><strong>|</strong><strong> </strong><strong>n</strong>,</p><p></p><p><u><a href="https://interviewquestions.tuteehub.com/tag/according-366619" style="font-weight:bold;" target="_blank" title="Click to know more about ACCORDING">ACCORDING</a> the question</u>,</p><p>➩ <strong>∠</strong><strong>3</strong><strong> </strong>= ∠1 = 80° ... opposite angle.</p><p>➩<strong> </strong><strong>∠</strong><strong>4</strong><strong> </strong>= ∠2 = 100° ... opposite angles.</p><p></p><p>➩<strong> </strong><strong>∠</strong><strong>5</strong><strong> </strong>= ∠3 = 80° ... alternate angles.</p><p>➩<strong> </strong><strong>∠</strong><strong>6</strong><strong> </strong>= ∠4 = 100° ... alternate angles.</p><p></p><p>➩<strong> </strong><strong>∠</strong><strong>7</strong><strong> </strong>= ∠1 = 100° ... <a href="https://interviewquestions.tuteehub.com/tag/exterior-447186" style="font-weight:bold;" target="_blank" title="Click to know more about EXTERIOR">EXTERIOR</a> angles.</p><p>➩<strong> </strong><strong>∠</strong><strong>8</strong><strong> </strong>= ∠2 = 80° ... exterior angles.</p></body></html>


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