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. The ratio of ∠x : ∠y is 3 : 5. Hence find the unknown angles. x y 60o ∠x : o ∠ y : o Answer:_______________ |
| 2) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 45o ∠x : o ∠ y : o Answer:_______________ |
| 3) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 5. Hence find the unknown angles. x y 12o ∠x : o ∠ y : o Answer:_______________ |
| 4) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 6. Hence find the unknown angles. x y 27o ∠x : o ∠ y : o Answer:_______________ |
| 5) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 8. Hence find the unknown angles. x y 20o ∠x : o ∠ y : o Answer:_______________ |
| 6) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 7. Hence find the unknown angles. x y 60o ∠x : o ∠ y : o Answer:_______________ |
| 7) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 27o ∠x : o ∠ y : o Answer:_______________ |
| 8) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 36o ∠x : o ∠ y : o Answer:_______________ |
| 9) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 54o ∠x : o ∠ y : o Answer:_______________ |
| 10) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 6. Hence find the unknown angles. x y 18o ∠x : o ∠ y : o Answer:_______________ |
| 1) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 5. Hence find the unknown angles. x y 60o ∠x : Answer: 45 o ∠ y : Answer: 75 o SOLUTION 1 : Step 1: ∠x = 3 units , ∠y = 5 units Step 2: 3 units + 5 units = 8 units Step 3: 180o - 60o = 120o Step 4: 8 units = 120o 1 unit = 120o ÷ 8 = 15o Step 5: ∠x (3 units) = 3 x 15o = 45o Step 6: ∠y (5 units) = 5 x 15o = 75o |
| 2) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 45o ∠x : Answer: 30 o ∠ y : Answer: 105 o SOLUTION 1 : Step 1: ∠x = 2 units , ∠y = 7 units Step 2: 2 units + 7 units = 9 units Step 3: 180o - 45o = 135o Step 4: 9 units = 135o 1 unit = 135o ÷ 9 = 15o Step 5: ∠x (2 units) = 2 x 15o = 30o Step 6: ∠y (7 units) = 7 x 15o = 105o |
| 3) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 5. Hence find the unknown angles. x y 12o ∠x : Answer: 63 o ∠ y : Answer: 105 o SOLUTION 1 : Step 1: ∠x = 3 units , ∠y = 5 units Step 2: 3 units + 5 units = 8 units Step 3: 180o - 12o = 168o Step 4: 8 units = 168o 1 unit = 168o ÷ 8 = 21o Step 5: ∠x (3 units) = 3 x 21o = 63o Step 6: ∠y (5 units) = 5 x 21o = 105o |
| 4) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 6. Hence find the unknown angles. x y 27o ∠x : Answer: 51 o ∠ y : Answer: 102 o SOLUTION 1 : Step 1: ∠x = 3 units , ∠y = 6 units Step 2: 3 units + 6 units = 9 units Step 3: 180o - 27o = 153o Step 4: 9 units = 153o 1 unit = 153o ÷ 9 = 17o Step 5: ∠x (3 units) = 3 x 17o = 51o Step 6: ∠y (6 units) = 6 x 17o = 102o |
| 5) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 8. Hence find the unknown angles. x y 20o ∠x : Answer: 32 o ∠ y : Answer: 128 o SOLUTION 1 : Step 1: ∠x = 2 units , ∠y = 8 units Step 2: 2 units + 8 units = 10 units Step 3: 180o - 20o = 160o Step 4: 10 units = 160o 1 unit = 160o ÷ 10 = 16o Step 5: ∠x (2 units) = 2 x 16o = 32o Step 6: ∠y (8 units) = 8 x 16o = 128o |
| 6) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 7. Hence find the unknown angles. x y 60o ∠x : Answer: 36 o ∠ y : Answer: 84 o SOLUTION 1 : Step 1: ∠x = 3 units , ∠y = 7 units Step 2: 3 units + 7 units = 10 units Step 3: 180o - 60o = 120o Step 4: 10 units = 120o 1 unit = 120o ÷ 10 = 12o Step 5: ∠x (3 units) = 3 x 12o = 36o Step 6: ∠y (7 units) = 7 x 12o = 84o |
| 7) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 27o ∠x : Answer: 34 o ∠ y : Answer: 119 o SOLUTION 1 : Step 1: ∠x = 2 units , ∠y = 7 units Step 2: 2 units + 7 units = 9 units Step 3: 180o - 27o = 153o Step 4: 9 units = 153o 1 unit = 153o ÷ 9 = 17o Step 5: ∠x (2 units) = 2 x 17o = 34o Step 6: ∠y (7 units) = 7 x 17o = 119o |
| 8) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 36o ∠x : Answer: 32 o ∠ y : Answer: 112 o SOLUTION 1 : Step 1: ∠x = 2 units , ∠y = 7 units Step 2: 2 units + 7 units = 9 units Step 3: 180o - 36o = 144o Step 4: 9 units = 144o 1 unit = 144o ÷ 9 = 16o Step 5: ∠x (2 units) = 2 x 16o = 32o Step 6: ∠y (7 units) = 7 x 16o = 112o |
| 9) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 2 : 7. Hence find the unknown angles. x y 54o ∠x : Answer: 28 o ∠ y : Answer: 98 o SOLUTION 1 : Step 1: ∠x = 2 units , ∠y = 7 units Step 2: 2 units + 7 units = 9 units Step 3: 180o - 54o = 126o Step 4: 9 units = 126o 1 unit = 126o ÷ 9 = 14o Step 5: ∠x (2 units) = 2 x 14o = 28o Step 6: ∠y (7 units) = 7 x 14o = 98o |
| 10) The following figure is made up of straight lines. The ratio of ∠x : ∠y is 3 : 6. Hence find the unknown angles. x y 18o ∠x : Answer: 54 o ∠ y : Answer: 108 o SOLUTION 1 : Step 1: ∠x = 3 units , ∠y = 6 units Step 2: 3 units + 6 units = 9 units Step 3: 180o - 18o = 162o Step 4: 9 units = 162o 1 unit = 162o ÷ 9 = 18o Step 5: ∠x (3 units) = 3 x 18o = 54o Step 6: ∠y (6 units) = 6 x 18o = 108o |