Lines Angles and Triangles - Test Questions

Question 1

Question:   Can two vertically opposite angles be supplement to each other? Draw a diagram to illustrate your answer.

Answer:   
Let AB and CD bisect each other at right angles as shown in figure.





( Vertically opposite angles can be
supplements to each other)

Question 1

Question:  

Answer:   



x and y


146 + y = 180

y = 180 - 146
= 34⁰
(vertically opposite angles)
2x = 34

x = 17^o

Question 3

Question:  

Answer:   
5x + 10 = 90^o
5x = 90^o - 10^o
= 80^o






Verification:

Question 4

Question:   In the following diagrams parallel lines are marked by arrows in the same direction. Transversal is also drawn. Find the missing angles and provide the reason for each.
Note: (No proof is required but the essential steps of working must be given)

Answer:    (i) Find a, b, c, d, e, f, g.








(ii) In the adjoining diagram AB||CD; PQ and RS are transversals. Find angles 1, 2, .....16.

Question 5

Question:   If two straight lines are each perpendicular to a third straight line then they are parallel to each other. Prove.

Answer:   

Straight line AB and CD are perpendicular to line l.

AB||CD

Question 6

Question:  

Answer:   







From (i), (ii) and (iii)

are supplementary angles.

Question 7

Question:  

Answer:   
AB||CD, BC||DE




AB||CD (given)
BC is a transversal

BC||DE (given)
DC is a transversal

Question 8

Question:   In the figure, show that AB||EF.

Answer:    [given]




i.e.,

Question 9

Question:   If a line is perpendicular to one of two given parallel lines, show that it is also perpendicular to the other line.

Answer:   







[corresponding angles]
But,

Question 10

Question:  
are the bisectors of the corresponding angles BGE and DHE respectively.
Show that

Answer:   

angles BGE and DHE respectively.




i)