Question 1: In the adjoining figure Find the values of . Give reasons.

Answer:

(Vertically opposite angles)

Hence

(Alternate interior angles)

Substituting in (i) we get

Hence

Question 2: In each of the following figures, Find. the value of . Give reasons

Answer:

i) Since

ii) , corresponding angles are equal therefore

Question 3: In the adjoining figure, are cut by a transversal, at respectively. If , find the measure of each one of the marked angles.

Answer:

Given

Therefore

Therefore

(Vertically opposite angles)

(Vertically opposite angles )

(Alternate angles)

(alternate angles)

Similarly

Question 4: In the adjoining figure , Find the values of .

Answer:

(Alternate interior angles)

Therefore

Therefore

Now (angles on straight lines are complementary)

Question 5: In each of the following figures, find, the value of in each case

Answer:

i) Given

Extend backwards

Therefore

ii)

Draw a line parallel to passing through point E

(Alternate angles)

Therefore

Similarly (Alternate angles)

Therefore

Hence

iii)

Draw a line parallel to

Therefore

(Alternate angles)

(Alternate angles)

Hence

iv)

Draw a line

(Corresponding angles)

Similarly

Or

Hence

v)

Therefore

(Corresponding angles)

vi)

Sum of interior angles

Question 6: In the adjoining figure, Find the values of

Answer:

Therefore

… … … … … i)

Also

Substituting in (i)

Sum of angles of a triangle

Therefore

Question 7: In each of the following figures, . Find the values of .

Answer:

i)

(Alternate angles)

Therefore

Similarly

(Alternate angles)

Since

(Angles of a triangle)

ii)

Question 8: In the given figure, Find the values of .

Answer:

(Vertically opposite angles )

(Alternate angles)

Therefore

Therefore

(angles on straight line)

Question 9: In the given figure, Find the values of .

Answer:

(alternate angles)

Therefore

(sum of corresponding angles)

(sum of angles of triangle)

(alternate angles)

Therefore

Question 10: In each of the following figures, find out for what value of will the lines be parallel to each other?

Answer:

i) For to be parallel

(Corresponding angles)

ii) For to be parallel

iii) For to be parallel

(corresponding angles)

iv) Given: (angles on a straight line )

For to be parallel

(corresponding angles)

or

Question 11: In the adjoining figure and they cut the line. respectively. Find the value of .

Answer:

(corresponding angles)

Therefore

Hence

Question 12: In the adjoining figure: .Find the value of .

Answer:

Given:

(corresponding angles)

(alternate angles)

Question 13: In the adjoining figure: .Find the value of

Answer:

Given

Draw a line

(alternate angles)

Similarly (alternate angles)

(Angles on a straight line)

Therefore

Hence

Question 14: In the adjoining figure cuts them at respectively. are bisectors of respectively. Prove that .

Answer:

Given

GP is angle bisector of

HQ is angle bisector of

Because

or

Now

(Alternate angles)

Hence

Question 15: In each of the following figures determine the values of: :

Answer:

i) Using corresponding angle and alternate angles

ii)

Hence

iii) (corresponding angles)

(corresponding angle)

(corresponding angles)

iv)

Hence

Question 16: State, giving reasons, whether or not. Given in (iii):

Answer:

i)

Hence

Alternate angles are equal

ii) Since

iii) Given

Therefore

But

Hence

iv)

Hence

Question 17: In the given figure and Prove that Prove that .

Answer:

Given

Hence (Corresponding angles are equal)

Hence