Question

In the adjoining figure. line p
line q. line / || line m. Find measures of Angle-a Angle-b and Angle-c, using the measures of given angles. Justify your answers​

Answer 1

Answer:

angle a= 100 degree

angle c=80 degrees

angle b=80 degrees

Step-by-step explanation

angle a we get by using vertically opposite angles and by using co interior angles.

angle b we get by using alternate interior angles and linear pair.

angle c we get by using corresponding angles property.

hope this helps you . stay home, stay safe .

Answer 2

Answer:

The measures of angles a, b and c are 100°, 80° and 80° respectively.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment for diagram.

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

Points A and B on line p.

Points C and D on line q.

Points P and Q on line l.

Points R and S on line m.

Lines AB and PQ intersect in point W.

Lines AB and RS intersect in point X.

Lines CD and PQ intersect in point Z.

Lines CD and RS intersect in point Y.

Now, line p || line q and l is transversal,

∴ m∠AWZ + m∠CZW = 180° - - [ Interior angles ]

⇒ 80° + m∠CZW = 180°

⇒ m∠CZW = 180° - 80°

∴ m∠CZW = 100°

Now, PQ and CD intersect in point Z,

∴ m∠QZY = m∠CZW - - [ Vertically opposite angles ]

∴ m∠QZY = 100°

∴ a = 100°

Now, line l || line m and p is transversal,

∴ m∠BXR = m∠AWZ - - [ Alternate exterior angles ]

∴ m∠BXR = 80°

∴ c = 80°

Now, line p || line q and line m is transversal,

∴ m∠XYD = m∠RXB - - [ Corresponding angles ]

∴ b = c

∴ b = 80°

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°.