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In the given figure if PQ || RS, 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. 42
  2. 74
  3. 106
  4. 126

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Option 1 : 42
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<p><strong>Given:</strong></p><p>PQ || RS (PQ is parallel to RS)</p><p>Angle 1 = (3x - 20)°</p><p>Angle 2 = (2x - 10)°</p><p><strong>Concept Used:</strong></p><p>When two parallel lines are intersected by a transversal, the consecutive interior angles are supplementary. This means that the sum of the measures of the consecutive interior angles is 180°.</p><p>In the given figure, the angles labeled (3x - 20)° and (2x - 10)° are consecutive interior angles.</p><p><strong>Calculation:</strong></p><p>According to the concept of consecutive interior angles:</p><p>(3x - 20)° + (2x - 10)° = 180°</p><p>Combine like terms:</p><p>3x + 2x - 20 - 10 = 180</p><p>5x - 30 = 180</p><p>5x = 180 + 30</p><p>5x = 210</p><p>x = 210 / 5</p><p>x = 42</p><p><strong>∴ The value of x is 42.</strong></p> - halleshangoutonline.com
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