Question
Download Solution PDFIn the adjoining figure if AB || CD then the value of x is -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
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°.
Last updated on Jun 2, 2025
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