Question

please answer this questions friends

Answer 1

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In the given figure, p || q, l and m are the transversal. Find x, y, z, u, v and w.

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• x = 50°
• y = 130°
• z = 130°
• u = 60°
• v = 60°
• w = 120°

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• p || q, l and m are transversal

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• value of x, y, z, u, v and w

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In this question, we will use some properties like :-

Vertically Opposite Angle

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertically opposite angles.

Alternate Interior Angle

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines.

Corresponding Angle

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Linear Pair

When the sum of two angles is 180° and they form a straight angle is known as linear pair.

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Let 60° be ∠1 and 130° be ∠2

∠1 = v = 60° [ Vertically Opposite Angles ]

∠2 = z = 130° [ Alternate Interior Angle ]

∠1 = u = 60° [ Alternate Interior Angle ]

∠2 = y = 130° [ Corresponding Angle ]

➞ z + x = 180° [ Linear Pair ]

➞ 130° + x = 180°

➞ x = 180° - 130°

➞ x = 50°

➞ u + w = 180° [ Linear Pair ]

➞ 60° + w = 180°

➞ w = 180° - 60°

➞ w = 120°

Therefore, value of x = 50°, y = 130°, z = 130°, u = 60°, v = 60° and w = 120°.

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Answer 2

Let 60° be ∠1 and 130° be ∠2

$∠1 = v = 60°$

[ Vertically Opposite Angles ]

$∠2 = z = 130°$

[ Alternate Interior Angle ]

$∠1 = u = 60°$

[ Alternate Interior Angle ]

$∠2 = y = 130°$

[ Corresponding Angle ]

$➞ z + x = 180°$

[ Linear Pair ]

$➞ 130° + x = 180°$

$➞ x = 180° - 130° \\ </strong></p><p></p><p><strong>[tex]➞ x = 180° - 130° \\ ➞ x = 50°$

$➞ u + w = 180°$

[ Linear Pair ]

$➞ 60° + w = 180° \\ </strong></p><p></p><p><strong>[tex]➞ 60° + w = 180° \\ ➞ w = 180° - 60° \\ </strong></p><p></p><p><strong>[tex]➞ 60° + w = 180° \\ ➞ w = 180° - 60° \\ ➞ w = 120°$

Therefore, value of

$x = 50°, \\ y = 130° , \\ z = 130°, \\ u = 60°, \\ v = 60° \\ and \\ \: w = 120°.$