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