Question

in the adjoining figure line p || line q Line t and line s are transversals . Find measure of angle x and angle y using the measures of angles given in the figure​

Answer 1

Answer:

Here is your required answer

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Step-by-step explanation:

angle x = 70. (corresponding angle)

angle y = 40. (alternate interior angle)

Answer 2

Answer:

The measure of ∠x is 140°.

The measure of ∠y is 110°.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment for the diagram.

In figure, we have to mark some points on the given lines.

Let the points on line p be P and Q.

The points on line q be L and M.

The points on line t be A and B.

The points on line s be C and D.

The lines t and p intersect in point W.

The lines s and p interest in point Z.

The lines t and q interest in point X.

The lines s and q interest in point Y.

Now, AB is a straight line.

∴ ∠AWZ + ∠ZWX = 180° - - [ Angles in linear pair ]

⇒ 40° + ∠ZWX = 180°

⇒ ∠ZWX = 180° - 40°

∴ ∠ZWX = 140°

Now, line p || line q and line t is transversal.

∴ m∠ZWX = m∠YXB - - [ Corresponding angles ]

⇒ m∠YXB = 140°

∴ x = 140°

Now, lines CD and LM intersect each other at point Y.

∴ m∠ZYX = m∠DYM - - [ Vertically opposite angles ]

∴ m∠ZYX = 70°

Now, lines p and q are parallel and line s is transversal,

∴ m∠ZYX + m∠WZY = 180°

⇒ 70° + m∠WZY = 180°

⇒ m∠WZY = 180° - 70°

⇒ m∠WZY = 110°

∴ y = 110°

Additional Information:

1. Parallel lines:

The lines which do not meet each other when extended are called as parallel lines.

2. Intersecting lines:

The lines which meet each other in a point are called as intersecting lines.

3. Transversal:

A line which divides one or more lines in two distinct parts is called a transversal.

4. Properties related to Parallel lines and Transversals:

A. Corresponding Angles Property

B. Alternate Angles Property

C. Interior Angles Property

5. Corresponding Angles Property:

The corresponding angles formed by parallel lines and their transversals are of equal measures.

6. Alternate Angles Property:

The alternate angles formed by parallel lines and their transversals are of equal measures.

7. Interior Angles Property:

The interior angles formed by parallel lines and their transversals are supplementary angles i. e. their sum is 180°.