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In the adjoining figure if AB || CD then the value of x is -

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Rajasthan 3rd Grade Level 1 Official Paper (Held On: 25 Feb, 2023 Shift 1)
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  1. 60 
  2. 80
  3. 90
  4. 100

Answer (Detailed Solution Below)

Option 4 : 100
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<p><strong>Given:</strong></p><p>AB || CD (AB is parallel to CD)</p><p>Angle between the transversal and AB = 80°</p><p>Angle between the other transversal and CD = 20°</p><p>Angle at O = x</p><p><strong>Concept Used:</strong></p><p>When two parallel lines are intersected by a transversal, the alternate interior angles are equal.</p><p>The sum of the angles in a triangle is 180°.</p><p><strong>Construction:</strong></p><p><amp-img alt="12-5-2025 IMG-1346 Shiwangani Gupta -(2)" src="/" height="141" width="192"></amp-img></p><p>Draw a line EF parallel to AB and CD passing through point O.</p><p><strong>Calculation:</strong></p><p>Since AB || EF, the alternate interior angles are equal.</p><p>Therefore, ∠BAO = ∠AOE = 80°</p><p>Since CD || EF, the alternate interior angles are equal.</p><p>Therefore, ∠DCO = ∠COF = 20°</p><p>Now, consider the angle at point O, which is x (∠AOC). This angle is the sum of ∠AOE and ∠COF.</p><p>x = ∠AOE + ∠COF</p><p>x = 80° + 20°</p><p>x = 100°</p><p><strong>∴ The value of x is 100°.</strong></p> - www.khautorepair.com
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