Question

In the adjoining figure line a is parallel to line b line l is a transversal find the measures of angle x angle Y angle Z using the given information ​

Answer 1

Answer:

angles

X=105°

Y=105°

Z=75°

Step-by-step explanation:

angles

X=105° (corresponding angles)

Y=105° (vertical opposite angles)

Z=75° (linear pair)

Answer 2

Answer:

The measures of angles x, y and z are 105°, 105° and 75° respectively.

Step-by-step-explanation:

We have to mark some points on the lines given in the figure.

Points A & B on line a.

Points C & D on line b.

Points L & M on line l.

Lines AB & LM intersect in point P.

Lines CD & LM intersect in point Q.

Now, line a || line b, and line l is a transversal,

∴ m∠PQC = m∠LPA - - [ Corresponding angles ]

∴ x = 105°

Now, lines CD & LM intersect in point Q,

∴ m∠PQC = m∠MQD - - [ Vertically opposite angles ]

∴ x = y

∴ y = 105°

Now, line AB is a straight line and line QN is on it,

∴ m∠MQD + m∠PQD = 180° - - [ Angles in linear pair ]

⇒ y + m∠PQD = 180°

⇒ 105° + m∠PQD = 180°

⇒ m∠PQD = 180° - 105°

⇒ m∠PQD = 75°

Now,

m∠PQD = m∠LPB - - [ Corresponding angles ]

∴ z = 75°

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°.