Q.1 In the adjoining figure Find the values of . Give reasons.

(Vertically opposite angles)

Hence

(Alternate interior angles)

Substituting in (i) we get

Hence

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

i) Since

ii) , corresponding angles are equal therefore

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

Given

Therefore

Therefore

(Vertically opposite angles)

(Vertically opposite angles )

(Alternate angles)

(alternate angles)

Similarly

Q.4 In the adjoining figure , Find the values of .

(Alternate interior angles)

Therefore

Therefore

Now (angles on straight lines are complementary)

Q.5 In each of the following figures, find, the value of in each case

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)

or

vi)

Sum of interior angles

Q.6 In the adjoining figure, Find the values of

Therefore

Also

or

Substituting in (i)

Sum of angles of a triangle

Therefore

Q.7 In each of the following figures, . Find the values of .

i)

(Alternate angles)

Therefore

Similarly

(Alternate angles)

Since

(Angles of a triangle)

ii)

Q.8 In the given figure, Find the values of .

(Vertically opposite angles )

(Alternate angles)

Therefore

Therefore

(angles on straight line)

Q.9 In the given figure, Find the values of .

(alternate angles)

Therefore

(sum of corresponding angles)

(sum of angles of triangle)

(alternate angles)

Therefore

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

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

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

(corresponding angles)

Therefore

Hence

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

Given:

(corresponding angles)

(alternate angles)

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

Given

Draw a line

(alternate angles)

Similarly (alternate angles)

(Angles on a straight line)

Therefore

Hence

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

Given

GP is angle bisector of

HQ is angle bisector of

Because

or

Now

(Alternate angles)

Hence

Q.15 In each of the following figures determine the values of: :

i) Using corresponding angle and alternate angles

ii)

Hence

iii) (corresponding angles)

(corresponding angle)

(corresponding angles)

iv)

Hence

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

i)

Hence

Alternate angles are equal

ii) Since

iii) Given

Therefore

But

Hence

iv)

Hence

Q.17 In the given figure and Prove that Prove that .

Given

Hence (Corresponding angles are equal)

Hence