Problems on Lines Angles - Test Questions-i

Question 11

Question:   In the given figure, each of the angles AOC and AOB are right angles. Show that BOC is a line.

Answer:   
=180^o

Since the sum of angles formed by them is 180^o, BOC is a line.

Question 12

Question:  

Answer:   


Multiplying by 2,



Hence A, O and B are collinear points.

Question 13

Question:   Prove that the bisectors of a pair of consecutive angles of two parallel lines are at right angles to one another.

Answer:   
AB||CD and EFGH is a transversal.




...(i) (consecutive interior angles)




= 90^o

i.e., the bisectors of a pair of consecutive interior angles are at right angles.

Question 14

Question:  

Answer:   


= 60^o



Therefore m and n are parallel.

Question 15

Question:  
Determine all the angles from 1 to 8.

Answer:   






= 36^o

=108^o

=72^o

Question 16

Question:   If two lines are intersected in such a way that bisectors of a pair of corresponding angles are parallel, show that the two lines are parallel.

Answer:   





iii)

Question 17

Question:   A transversal intersects two given lines in such a way that the interior angles on the same side of transversal are equal. Show by means of a figure that the lines need not be parallel. State the condition under which the two lines will be parallel.

Answer:   

Question 18

Question:   If the angles of a triangle are in the ratio 2:3:4, determine the three angles.

Answer:    Let the three angles of the triangle be 2x^o, 3x^o and 4x^o.

2x^o+3x^o+4x^o= 180 ^o (Angle sum property )
9x^o= 180^o

x^o= 20^o
The angles measure 2x^o= 2 x 20^o
= 40^o
3x^o= 3 x 20^o
= 60^o
4x^o= 4 x 20^o
= 80^o
The three angles of the triangle in the ratio 2:3:4 are 40^o, 60^o, 80^o.

Question 19

Question:   Can a triangle have
i) two right angles?
ii) two obtuse angles?
iii) two acute angles?
iv) all angles more than 60^o?
v) all angles less than 60^o?
vi) all angles equal to 60^o?

Answer:    i) No. The sum of those two angles itself becomes 180^o.
ii) No. The sum of two obtuse angles will always be greater than 180^o.
iii) Yes. The sum of two acute angles will always be less than 180^o.
iv) No. The sum of all three angles will be more than 180^o .
v) No. The sum of 3 angles will be less than 180^o .
Vi) Yes. The sum of 3 angles, each of 60^o amounts to 180^o.

Question 20

Question:  

Answer:   





(Exterior angle = sum of interior opposite angles)

(Exterior angle = sum of interior opposite angles)
Adding (i) and (ii),