Scroll:Geometry >> Triangles >> ps (1559)

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)  
33°
111°
18°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 18° and∠ ABD = 33°. 

Find ∠ DFE.

o


Answer:_______________




2)  
32°
113°
21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 32°. 

Find ∠ DFE.

o


Answer:_______________




3)  
31°
106°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 31°. 

Find ∠ DFE.

o


Answer:_______________




4)  
37°
113°
16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 37°. 

Find ∠ DFE.

o


Answer:_______________




5)  
31°
110°
19°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 19° and∠ ABD = 31°. 

Find ∠ DFE.

o


Answer:_______________




6)  
38°
113°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 38°. 

Find ∠ DFE.

o


Answer:_______________




7)  
40°
116°
16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 40°. 

Find ∠ DFE.

o


Answer:_______________




8)  
37°
112°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 37°. 

Find ∠ DFE.

o


Answer:_______________




9)  
36°
118°
22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 36°. 

Find ∠ DFE.

o


Answer:_______________




10)  
31°
112°
21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 31°. 

Find ∠ DFE.

o


Answer:_______________




 

1)  
33°
111°
18°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 18° and∠ ABD = 33°. 

Find ∠ DFE.

Answer: 111o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 33 o = 27o

Step 3: ∠ FCB = 60 o - 18 o = 42o

Step 4: ∠ BFC = 180 o - 27 o - 42 o = 111o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 111o (vertically opposite angles)



2)  
32°
113°
21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 32°. 

Find ∠ DFE.

Answer: 113o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 32 o = 28o

Step 3: ∠ FCB = 60 o - 21 o = 39o

Step 4: ∠ BFC = 180 o - 28 o - 39 o = 113o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 113o (vertically opposite angles)



3)  
31°
106°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 31°. 

Find ∠ DFE.

Answer: 106o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 31 o = 29o

Step 3: ∠ FCB = 60 o - 15 o = 45o

Step 4: ∠ BFC = 180 o - 29 o - 45 o = 106o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 106o (vertically opposite angles)



4)  
37°
113°
16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 37°. 

Find ∠ DFE.

Answer: 113o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 37 o = 23o

Step 3: ∠ FCB = 60 o - 16 o = 44o

Step 4: ∠ BFC = 180 o - 23 o - 44 o = 113o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 113o (vertically opposite angles)



5)  
31°
110°
19°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 19° and∠ ABD = 31°. 

Find ∠ DFE.

Answer: 110o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 31 o = 29o

Step 3: ∠ FCB = 60 o - 19 o = 41o

Step 4: ∠ BFC = 180 o - 29 o - 41 o = 110o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 110o (vertically opposite angles)



6)  
38°
113°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 38°. 

Find ∠ DFE.

Answer: 113o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 38 o = 22o

Step 3: ∠ FCB = 60 o - 15 o = 45o

Step 4: ∠ BFC = 180 o - 22 o - 45 o = 113o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 113o (vertically opposite angles)



7)  
40°
116°
16°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 16° and∠ ABD = 40°. 

Find ∠ DFE.

Answer: 116o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 40 o = 20o

Step 3: ∠ FCB = 60 o - 16 o = 44o

Step 4: ∠ BFC = 180 o - 20 o - 44 o = 116o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 116o (vertically opposite angles)



8)  
37°
112°
15°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 15° and∠ ABD = 37°. 

Find ∠ DFE.

Answer: 112o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 37 o = 23o

Step 3: ∠ FCB = 60 o - 15 o = 45o

Step 4: ∠ BFC = 180 o - 23 o - 45 o = 112o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 112o (vertically opposite angles)



9)  
36°
118°
22°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 22° and∠ ABD = 36°. 

Find ∠ DFE.

Answer: 118o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 36 o = 24o

Step 3: ∠ FCB = 60 o - 22 o = 38o

Step 4: ∠ BFC = 180 o - 24 o - 38 o = 118o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 118o (vertically opposite angles)



10)  
31°
112°
21°

The figure is not drawn to scale.
ABC is an equilateral triangle.
EC and BD are straight lines.
∠ACE = 21° and∠ ABD = 31°. 

Find ∠ DFE.

Answer: 112o


SOLUTION 1 :

Step 1: ∠ ABC = ∠  ACB = 60o (equilateral triangle)

Step 2: ∠ FBC = 60 o - 31 o = 29o

Step 3: ∠ FCB = 60 o - 21 o = 39o

Step 4: ∠ BFC = 180 o - 29 o - 39 o = 112o (sum of angles in a triangle)

Step 5: ∠ DFE =  ∠ BFC = 112o (vertically opposite angles)