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in Plane Geometry and Line and Angle by (34.1k points)
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In the given figure, AB || CD, if ∠OAB = 58° and ∠OCD = 45° then find the value of x.

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We are given that AB || CD and ∠OAB = 58° and ∠OCD = 42°.

Construction: Draw a line PQ || AB || CD

To find: x

PQ || AB (by construction)

⇒ ∠AOP = ∠OAB = 58° (alternate angle)

∴ ∠COP = ∠OCD = 42° (alternate angle)

∴ ∠AOC = ∠AOP + ∠COP = 58° + 42°

⇒ ∠AOC = 100°

Thus, reflex ∠AOC

x = 360° – ∠AOC 

= 360° – 100° = 260°

Hence, x = 260°

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