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

12-5-2025 IMG-1346 Shiwangani Gupta -(1)

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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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Rajasthan 3rd Grade (Level 1) Full Test 11
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Detailed Solution

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Given:

AB || CD (AB is parallel to CD)

Angle between the transversal and AB = 80°

Angle between the other transversal and CD = 20°

Angle at O = x

Concept Used:

When two parallel lines are intersected by a transversal, the alternate interior angles are equal.

The sum of the angles in a triangle is 180°.

Construction:

12-5-2025 IMG-1346 Shiwangani Gupta -(2)

Draw a line EF parallel to AB and CD passing through point O.

Calculation:

Since AB || EF, the alternate interior angles are equal.

Therefore, ∠BAO = ∠AOE = 80°

Since CD || EF, the alternate interior angles are equal.

Therefore, ∠DCO = ∠COF = 20°

Now, consider the angle at point O, which is x (∠AOC). This angle is the sum of ∠AOE and ∠COF.

x = ∠AOE + ∠COF

x = 80° + 20°

x = 100°

∴ The value of x is 100°.

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