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In the given figure, AB || CD || EF. Find x, y and z.

In the given figure, AB || CD || EF. Find x, y and z. Lines and Angles, Foundation Mathematics R.S. Aggarwal ICSE Class 7.

Lines & Angles

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Answer

Consider AB || CD and AD is a transversal:

x° = 140° \quad[Alternate angles]

Since, x°, y° and 120° meet at same point D and form a complete angle:

x° + y° + 120° = 360°

⇒ 140° + y° + 120° = 360° \quad[Substituting the value of x]

⇒ 260° + y° = 360°

⇒ y° = 360° - 260°

⇒ y° = 100°

y° and z° are co-interior angles.

Co-interior angles are supplementary:

∴ y° + z° = 180°

⇒ 100° + z° = 180° \quad[Substituting the value of y]

⇒ z° = 180° - 100°

⇒ z° = 80°

x° = 140°, y° = 100° and z° = 80°

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