Scroll:geometry >> Angles >> saq (625)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
72°
z

∠ x : 
∠ y : 
∠ z :   



Answer:_______________




2)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
138°
y

∠ x : 
∠ y :   



Answer:_______________




3)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
51°
39°

∠ x : 

∠ y : 



Answer:_______________




4)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
64°
z

∠ x : 
∠ y : 
∠ z :   



Answer:_______________




5)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
129°
y

∠ x : 
∠ y :   



Answer:_______________




6)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
66°
40°

∠ x : 

∠ y : 



Answer:_______________




7)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
76°
z

∠ x : 
∠ y : 
∠ z :   



Answer:_______________




8)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
132°
y

∠ x : 
∠ y :   



Answer:_______________




9)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
52°
39°

∠ x : 

∠ y : 



Answer:_______________




10)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
60°
z

∠ x : 
∠ y : 
∠ z :   



Answer:_______________




 

1)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
72°
z

∠ x :  Answer: 81°
∠ y :  Answer: 27°
∠ z :  Answer: 81° 



SOLUTION 1 :

Step 1: ∠ x =∠ z  (vertically opposite angle)

Step 2: 4 units = 180o - 72° (∠s on a straight line)

                        = 108o
Step 3: 1 unit = 108o ÷ 4

                      = 27o
Step 4: ∠ x = 2 x 27o

                    = 81°

            ∠ y = 27°

            ∠ z = 81°



2)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
138°
y

∠ x :  Answer: 28°
∠ y :  Answer: 14° 



SOLUTION 1 :

Step 1: 3 units = 180o - 138° (∠s on a straight line)

                        = 42o
Step 2: 1 unit = 42o ÷ 3

                      = 14o
Step 3: ∠ x = 2 x 14o

                    = 28°

            ∠ y = 14°



3)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
51°
39°

∠ x :  Answer: 39°

∠ y :  Answer: 90°


SOLUTION 1 :

Step 1: ∠x = 39° (vertically opposite angle)

Step 2: ∠y = 180o - 39° - 51° = 90°

 



4)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
64°
z

∠ x :  Answer: 87°
∠ y :  Answer: 29°
∠ z :  Answer: 87° 



SOLUTION 1 :

Step 1: ∠ x =∠ z  (vertically opposite angle)

Step 2: 4 units = 180o - 64° (∠s on a straight line)

                        = 116o
Step 3: 1 unit = 116o ÷ 4

                      = 29o
Step 4: ∠ x = 2 x 29o

                    = 87°

            ∠ y = 29°

            ∠ z = 87°



5)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
129°
y

∠ x :  Answer: 34°
∠ y :  Answer: 17° 



SOLUTION 1 :

Step 1: 3 units = 180o - 129° (∠s on a straight line)

                        = 51o
Step 2: 1 unit = 51o ÷ 3

                      = 17o
Step 3: ∠ x = 2 x 17o

                    = 34°

            ∠ y = 17°



6)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
66°
40°

∠ x :  Answer: 40°

∠ y :  Answer: 74°


SOLUTION 1 :

Step 1: ∠x = 40° (vertically opposite angle)

Step 2: ∠y = 180o - 40° - 66° = 74°

 



7)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
76°
z

∠ x :  Answer: 78°
∠ y :  Answer: 26°
∠ z :  Answer: 78° 



SOLUTION 1 :

Step 1: ∠ x =∠ z  (vertically opposite angle)

Step 2: 4 units = 180o - 76° (∠s on a straight line)

                        = 104o
Step 3: 1 unit = 104o ÷ 4

                      = 26o
Step 4: ∠ x = 2 x 26o

                    = 78°

            ∠ y = 26°

            ∠ z = 78°



8)  

The following figure is made up of straight lines. Find the unknown angles. Given that ∠ x is twice that of ∠ y. Find the unknown angles. 

x
132°
y

∠ x :  Answer: 32°
∠ y :  Answer: 16° 



SOLUTION 1 :

Step 1: 3 units = 180o - 132° (∠s on a straight line)

                        = 48o
Step 2: 1 unit = 48o ÷ 3

                      = 16o
Step 3: ∠ x = 2 x 16o

                    = 32°

            ∠ y = 16°



9)  

The following figure is made up of straight lines. Find the unknown angles. 

y
x
52°
39°

∠ x :  Answer: 39°

∠ y :  Answer: 89°


SOLUTION 1 :

Step 1: ∠x = 39° (vertically opposite angle)

Step 2: ∠y = 180o - 39° - 52° = 89°

 



10)  

The following figure is made up of straight lines. Given that ∠ x is thrice that of ∠ y. Find the unknown angles.



y
x
60°
z

∠ x :  Answer: 90°
∠ y :  Answer: 30°
∠ z :  Answer: 90° 



SOLUTION 1 :

Step 1: ∠ x =∠ z  (vertically opposite angle)

Step 2: 4 units = 180o - 60° (∠s on a straight line)

                        = 120o
Step 3: 1 unit = 120o ÷ 4

                      = 30o
Step 4: ∠ x = 2 x 30o

                    = 90°

            ∠ y = 30°

            ∠ z = 90°