Scroll:Geometry >> Angles >> ps (3084)

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)  

∠AFB=86°. ∠FDC=106°. ∠BCD=93° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.



∠BEC °


∠ABE °


Answer:_______________




2)  

∠AFB=87°. ∠FDC=130°. ∠BCD=100° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




3)  

∠AFB=83°. ∠FDC=102°. ∠BCD=99° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




4)  

∠AFB=81°. ∠FDC=127°. ∠BCD=92° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




5)  

∠AFB=80°. ∠FDC=123°. ∠BCD=93° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




6)  

∠AFB=82°. ∠FDC=116°. ∠BCD=94° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




7)  

∠AFB=83°. ∠FDC=107°. ∠BCD=94° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




8)  

∠AFB=82°. ∠FDC=128°. ∠BCD=96° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




9)  

∠AFB=81°. ∠FDC=101°. ∠BCD=100° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




10)  

∠AFB=85°. ∠FDC=121°. ∠BCD=98° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC °

∠ABE °


Answer:_______________




 

1)  

∠AFB=86°. ∠FDC=106°. ∠BCD=93° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.



∠BEC Answer: 20°


∠ABE Answer: 20°


SOLUTION 1 :

Step 1: ∠DFE = 86° (opposite angle)

Step 2: ∠FDE = 180° - 106° (sum of angles on a straight line)

                       = 74°

Step 3: ∠BEC = 180° - 86° - 74° (sum of angles of triangle)

                       = 20°

Step 4: ∠BAD = 180° - 106° (AB // DC)

                       = 74°

Step 5: ∠ABE = 180° - 74° - 86° (sum of angles of triangle)

                       = 20°



2)  

∠AFB=87°. ∠FDC=130°. ∠BCD=100° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 43°

∠ABE Answer: 43°


SOLUTION 1 :

Step 1: ∠DFE = 87° (opposite angle)

Step 2: ∠FDE = 180° - 130° (sum of angles on a straight line)

                       = 50°

Step 3: ∠BEC = 180° - 87° - 50° (sum of angles of triangle)

                       = 43°

Step 4: ∠BAD = 180° - 130° (AB // DC)

                       = 50°

Step 5: ∠ABE = 180° - 50° - 87° (sum of angles of triangle)

                       = 43°



3)  

∠AFB=83°. ∠FDC=102°. ∠BCD=99° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 19°

∠ABE Answer: 19°


SOLUTION 1 :

Step 1: ∠DFE = 83° (opposite angle)

Step 2: ∠FDE = 180° - 102° (sum of angles on a straight line)

                       = 78°

Step 3: ∠BEC = 180° - 83° - 78° (sum of angles of triangle)

                       = 19°

Step 4: ∠BAD = 180° - 102° (AB // DC)

                       = 78°

Step 5: ∠ABE = 180° - 78° - 83° (sum of angles of triangle)

                       = 19°



4)  

∠AFB=81°. ∠FDC=127°. ∠BCD=92° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 46°

∠ABE Answer: 46°


SOLUTION 1 :

Step 1:

 ∠DFE = 81° (opposite angle)

Step 2:

 ∠FDE = 180° - 127° (sum of angles on a straight line)
   

= 53°

Step 3:

 ∠BEC = 180° - 81° - 53° (sum of angles of triangle)
   

= 46°

Step 4:

 ∠BAD = 180° - 127° (AB // DC)
   

= 53°

Step 5:

 ∠ABE = 180° - 53° - 81° (sum of angles of triangle)
   

= 46°


5)  

∠AFB=80°. ∠FDC=123°. ∠BCD=93° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 43°

∠ABE Answer: 43°


SOLUTION 1 :

Step 1: ∠DFE = 80° (opposite angle)

Step 2: ∠FDE = 180° - 123° (sum of angles on a straight line)

                       = 57°

Step 3: ∠BEC = 180° - 80° - 57° (sum of angles of triangle)

                       = 43°

Step 4: ∠BAD = 180° - 123° (AB // DC)

                       = 57°

Step 5: ∠ABE = 180° - 57° - 80° (sum of angles of triangle)

                       = 43°



6)  

∠AFB=82°. ∠FDC=116°. ∠BCD=94° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 50°

∠ABE Answer: 50°


SOLUTION 1 :

Step 1: ∠DFE = 81° (opposite angle)

Step 2: ∠FDE = 180° - 131° (sum of angles on a straight line)

                       = 49°

Step 3: ∠BEC = 180° - 81° - 49° (sum of angles of triangle)

                       = 50°

Step 4: ∠BAD = 180° - 131° (AB // DC)

                       = 49°

Step 5: ∠ABE = 180° - 39° - 81° (sum of angles of triangle)

                       = 50°



7)  

∠AFB=83°. ∠FDC=107°. ∠BCD=94° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 24°

∠ABE Answer: 24°


SOLUTION 1 :

Step 1: ∠DFE = 83° (opposite angle)

Step 2: ∠FDE = 180° - 107° (sum of angles on a straight line)

                       = 73°

Step 3: ∠BEC = 180° - 83° - 73° (sum of angles of triangle)

                       = 24°

Step 4: ∠BAD = 180° - 107° (AB // DC)

                       = 73°

Step 5: ∠ABE = 180° - 73° - 83° (sum of angles of triangle)

                       = 24°



8)  

∠AFB=82°. ∠FDC=128°. ∠BCD=96° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 46°

∠ABE Answer: 46°


SOLUTION 1 :

Step 1: ∠DFE = 82° (opposite angle)

Step 2: ∠FDE = 180° - 128° (sum of angles on a straight line)

                       = 52°

Step 3: ∠BEC = 180° - 82° - 52° (sum of angles of triangle)

                       = 46°

Step 4: ∠BAD = 180° - 128° (AB // DC)

                       = 52°

Step 5: ∠ABE = 180° - 52° - 82° (sum of angles of triangle)

                       = 46°



9)  

∠AFB=81°. ∠FDC=101°. ∠BCD=100° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 20°

∠ABE Answer: 20°


SOLUTION 1 :

Step 1: ∠DFE = 81° (opposite angle)

Step 2: ∠FDE = 180° - 101° (sum of angles on a straight line)

                       = 79°

Step 3: ∠BEC = 180° - 82° - 79° (sum of angles of triangle)

                       = 20°

Step 4: ∠BAD = 180° - 101° (AB // DC)

                       = 79°

Step 5: ∠ABE = 180° - 79° - 81° (sum of angles of triangle)

                       = 20°



10)  

∠AFB=85°. ∠FDC=121°. ∠BCD=98° and AB//EC. AFD, EFB and EDC are straight lines. Find ∠ABE and ∠BEC.

∠BEC Answer: 36°

∠ABE Answer: 36°


SOLUTION 1 :

Step 1: ∠DFE = 85° (opposite angle)

Step 2: ∠FDE = 180° - 121° (sum of angles on a straight line)

                       = 59°

Step 3: ∠BEC = 180° - 85° - 59° (sum of angles of triangle)

                       = 36°

Step 4: ∠BAD = 180° - 121° (AB // DC)

                       = 59°

Step 5: ∠ABE = 180° - 59° - 85° (sum of angles of triangle)

                       = 36°