Scroll:Geometry >> Angles >> ps (3085)

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)  

∠GJH=30°. ∠HIK=130°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




2)  

∠GJH=55°. ∠HIK=122°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




3)  

∠GJH=50°. ∠HIK=100°. GH//JI and HI=JI. JIk is straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




4)  

∠GJH=73°. ∠HIK=110°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




5)  

∠GJH=33°. ∠HIK=146°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




6)  

∠GJH=30°. ∠HIK=150°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




7)  

∠GJH=36°. ∠HIK=104°. GH//JI and HI=JI. JIK is a straight lines. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




8)  

∠GJH=46°. ∠HIK=152°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




9)  

∠GJH=59°. ∠HIK=114°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




10)  

∠GJH=60°. ∠HIK=100°. GH//JI and HI=JI. JIk is straight line. Find ∠JGH and ∠JHI.

∠JGH °

∠JHI °


Answer:_______________




 

1)  

∠GJH=30°. ∠HIK=130°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 85°

∠JHI Answer: 65°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 130° (sum of angles on a straight line)

                     = 50°

Step 2: ∠HJI + ∠JHI = 180° - 50° (sum of angles of triangle)

                                = 130°

Step 3: ∠JHI = 130° ÷ 2 (isosceles triangle)

                     = 65°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 65° 

Step 5: ∠JGH = 180° - 30° - 65° (GH // JI)

                      = 85°



2)  

∠GJH=55°. ∠HIK=122°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 64°

∠JHI Answer: 61°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 122° (sum of angles on a straight line)

                     = 58°

Step 2: ∠HJI + ∠JHI = 180° - 58° (sum of angles of triangle)

                                = 122°

Step 3: ∠JHI = 122° ÷ 2 (isosceles triangle)

                     = 61°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 61° 

Step 5: ∠JGH = 180° - 55° - 61° (GH // JI)

                      = 64°



3)  

∠GJH=50°. ∠HIK=100°. GH//JI and HI=JI. JIk is straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 80°

∠JHI Answer: 50°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 100° (sum of angles on a straight line)

                     = 80°

Step 2: ∠HJI + ∠JHI = 180° - 80° (sum of angles of triangle)

                                = 100°

Step 3: ∠JHI = 100° ÷ 2 (isosceles triangle)

                     = 50°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 50° 

Step 5: ∠JGH = 180° - 50° - 50° (GH // JI)

                      = 80°



4)  

∠GJH=73°. ∠HIK=110°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 52°

∠JHI Answer: 55°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 110° (sum of angles on a straight line)

                     = 70°

Step 2: ∠HJI + ∠JHI = 180° - 70° (sum of angles of triangle)

                                = 110°

Step 3: ∠JHI = 110° ÷ 2 (isosceles triangle)

                     = 55°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 55° 

Step 5: ∠JGH = 180° - 73° - 55° (GH // JI)

                      = 52°



5)  

∠GJH=33°. ∠HIK=146°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 74°

∠JHI Answer: 73°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 146° (sum of angles on a straight line)

                     = 34°

Step 2: ∠HJI + ∠JHI = 180° - 34° (sum of angles of triangle)

                                = 146°

Step 3: ∠JHI = 146° ÷ 2 (isosceles triangle)

                     = 73°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 73° 

Step 5: ∠JGH = 180° - 33° - 73° (GH // JI)

                      = 74°



6)  

∠GJH=30°. ∠HIK=150°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 75°

∠JHI Answer: 75°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 150° (sum of angles on a straight line)

                     = 30°

Step 2: ∠HJI + ∠JHI = 180° - 30° (sum of angles of triangle)

                                = 150°

Step 3: ∠JHI = 150° ÷ 2 (isosceles triangle)

                     = 75°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 75° 

Step 5: ∠JGH = 180° - 30° - 75° (GH // JI)

                      = 75°



7)  

∠GJH=36°. ∠HIK=104°. GH//JI and HI=JI. JIK is a straight lines. Find ∠JGH and ∠JHI.

∠JGH Answer: 92°

∠JHI Answer: 52°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 104° (sum of angles on a straight line)

                     = 76°

Step 2: ∠HJI + ∠JHI = 180° - 76° (sum of angles of triangle)

                                = 104°

Step 3: ∠JHI = 104° ÷ 2 (isosceles triangle)

                     = 52°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 52° 

Step 5: ∠JGH = 180° - 36° - 52° (GH // JI)

                      = 92°



8)  

∠GJH=46°. ∠HIK=152°. GH//JI and HI=JI. JIK is a straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 58°

∠JHI Answer: 76°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 152° (sum of angles on a straight line)

                     = 28°

Step 2: ∠HJI + ∠JHI = 180° - 28° (sum of angles of triangle)

                                = 152°

Step 3: ∠JHI = 152° ÷ 2 (isosceles triangle)

                     = 76°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 76° 

Step 5: ∠JGH = 180° - 46° - 76° (GH // JI)

                      = 58°



9)  

∠GJH=59°. ∠HIK=114°. GH//JI and HI=JI. JIK is straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 64°

∠JHI Answer: 57°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 114° (sum of angles on a straight line)

                     = 66°

Step 2: ∠HJI + ∠JHI = 180° - 66° (sum of angles of triangle)

                                = 114°

Step 3: ∠JHI = 114° ÷ 2 (isosceles triangle)

                     = 57°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 57° 

Step 5: ∠JGH = 180° - 57° - 59° (GH // JI)

                      = 64°



10)  

∠GJH=60°. ∠HIK=100°. GH//JI and HI=JI. JIk is straight line. Find ∠JGH and ∠JHI.

∠JGH Answer: 70°

∠JHI Answer: 50°


SOLUTION 1 :

Step 1: ∠HIJ = 180° - 100° (sum of angles on a straight line)

                     = 80°

Step 2: ∠HJI + ∠JHI = 180° - 80° (sum of angles of triangle)

                                = 100°

Step 3: ∠JHI = 100° ÷ 2 (isosceles triangle)

                     = 50°

Step 4: ∠JHI = ∠HJI (isosceles triangle)

                    = 50° 

Step 5: ∠JGH = 180° - 60° - 50° (GH // JI)

                      = 70°