Question 1: In the adjourning figure, name:
i)six points
ii) five line segments
iii) four rays
iv) four lines
v) four collinear points
Answer:
i) The point are
ii) Five line segments are
iii) Four Rays are
iv) Four lines are
v) Four Collinear points are
Question 2: In the adjoining figure, name :
i) two pairs of intersecting lines and their corresponding points of intersection
ii) three concurrent lines and their points of concurrence
iii) three rays
iv) two line segments
Answer:
i) Two points of intersecting lines are
intersecting at R
intersecting at Q.
ii) Three concurrent lines and their point of concurrence.
and point of concurrence is R
iii) Three rays are, some other rays are
, etc.
iv) Two line segments are
Question 3: State whether the following statements are true or false :
Answer:
i) A ray has no end Point:
ii) A line AB is the same as line BA:
iii) A ray AB is the same as BA:
iv) A line has a definite length:
v) Two planes always meet in a line:
vi) A plane has length and breadth but no thickness:
vii) Two distinct points always determine a unique line:
viii) Two lines may intersect in two points:
ix) Two intersecting lines cannot be both parallel to the same line:
Question 4: Two adjacent angles on a straight line are Find i) the value of
ii) the measure of each angle
Answer:
i)
ii) Hence
Question 5: Two adjacent angles on a straight line are – Find : i) the value of
ii) the measure of each angle
Answer:
i)
ii) The measure of angles
Question 6: Two adjacent angles on a straight line are in the ratio . Find the measure of each angle:
Answer:
The ratio of angles
Therefore the angles are and
The two angles are
Question 7: In the adjoining figure, is a straight line. Find the value
. Hence ,find,
Answer:
Therefore
And
Question 8: In the adjoining figure, AOB is a straight line. If , find the values of
and
.
Answer:
Therefore
Or Therefore
Question 9: In the adjoining figure, what value of make AOB a straight line?
Answer:
For to be a straight line
Question 10: In the adjoining figure, find the value of .
Answer:
Question 11: In each of the following figures, two lines intersect at a point
. Find the value of
Answer:
i) (vertically opposite angle)
We could have also used
ii) (vertically Opposite angles)
(Angles on a straight line are supplementary)
(Vertically opposite angles)
iii) (Vertically opposite angles)
(Angles on a straight line)
(Vertically opposite angles)
iv)
(Vertically opposite angles)
(Vertically opposite angles)
Substituting (ii) in (i)
From iii)
Question 12: Prove that the bisectors of two adjacent supplementary angles include a right angle.
Answer:
Let
Bisector of
Bisector of
Therefore
Hence
Question 13: Find the measure of an angle which is (i) equal to its complement (ii) equal to its supplement.
Answer:
i) If the , it’s complement
If
ii) If the , its supplement
Question 14: Find the angle which is more than its complement.
Answer:
Let the angle
Complement
Given
Question 15: Find the angle which is less than its complement.
Answer:
Let the angle
Complement
Given
Question 16: Find the angle which is more than its supplement.
Answer:
Let the angle
Supplement
Given
Question 17: Find the angle which is less than its supplement.
Answer:
Let the angle
Supplement
Given,
Question 18: Find the angle which is four times its complement.
Answer:
Let the angle
Complement
Given
Question 19: Find the angle which is five times its supplement.
Answer:
Let the angle
Complement
Given
Question 20: Find the angle whose supplement is four times its complement.
Answer:
Let the angle
Complement
Supplement
Given,
Question 21: Find the angle whose complement is one third of its supplement.
Answer:
Let the angle
Therefore Complement
Therefore Supplement
Given
Question 22: Two complementary angles are in the ratio Find the angles.
Answer:
Let the angle
Complement
Given
The complement
Hence the angles are
Question 23: Two supplementary angles are in the ratio 7. Find the angles.
Answer:
Let the angle
Supplement
Given
Hence the angles are
Question 24: Find the measure of an angle, if seven times its complement is less than three times its supplement.
Answer:
Let the angle
Complement Supplement
Given