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