**Chapter 4 Angles and Pairs of Angles Set 4.3**

Question 1.

Write the measures of the supplements of the angles given below:

i. 15Â°

ii. 85Â°

iii. 120Â°

iv. 37Â°

v. 108Â°

vi. 0Â°

vii. aÂ°

Solution:

i. Let the measure of the supplementary angle be xÂ°.

âˆ´ 15 + x = 180

âˆ´ 15 + x â€“ 15 = 180 â€“ 15

â€¦.(Subtracting 15 from both sides)

âˆ´ x = 165

âˆ´ The measures of the supplement of an angle of 15Â° is 165Â°.

ii. Let the measure of the supplementary angle be xÂ°.

âˆ´ 85 + x = 180

âˆ´ 85 + x â€“ 85 = 180 â€“ 85

â€¦.(Subtracting 85 from both sides)

âˆ´ x = 95

âˆ´ The measures of the supplement of an angle of 85Â° is 95Â°.

iii. Let the measure of the supplementary angle be xÂ°.

âˆ´ 120 + x = 180

âˆ´ 120 + x â€“ 120 = 180 â€“ 120

â€¦.(Subtracting 120 from both sides)

âˆ´ x = 60

âˆ´ The measures of the supplement of an angle of 120Â° is 60Â°.

iv. Let the measure of the supplementary angle be xÂ°.

âˆ´ 37 + x = 180

âˆ´ 37 + x â€“ 37 = 180 â€“ 37

â€¦.(Subtracting 37 from both sides)

âˆ´ x = 143

âˆ´ The measures of the supplement of an angle of 37Â° is 143Â°.

v. Let the measure of the supplementary angle be xÂ°.

âˆ´ 108 + x = 180

âˆ´ 108 + x â€“ 108 = 180 â€“ 108

â€¦.(Subtracting 108 from both sides)

âˆ´ x = 72

âˆ´ The measures of the supplement of an angle of 108Â° is 72Â°.

vi. Let the measure of the supplementary angle be xÂ°.

âˆ´0 + x = 180

âˆ´ x = 180

âˆ´ The measures of the supplement of an angle of 0Â° is 180Â°.

vii. Let the measure of the supplementary angle be xÂ°.

âˆ´ a + x = 180

âˆ´ a + x â€“ a = 180 â€“ a

â€¦.(Subtracting a from both sides) x = (180 â€“ a)

âˆ´ The measures of the supplement of an angle of aÂ° is (180 â€“ a)Â°.

Question 2.

The measures of some angles are given below. Use them to make pairs of complementary and supplementary angles.

mâˆ B = 60Â°

mâˆ N = 30Â°

mâˆ Y = 90Â°

mâˆ J = 150Â°

mâˆ D = 75Â°

mâˆ E = 0Â°

mâˆ F = 15Â°

mâˆ G = 120Â°

Solution:

i. mâˆ B + mâˆ N = 60Â° + 30Â°

= 90Â°

âˆ´âˆ B and âˆ N are a pair of complementary angles.

ii. mâˆ Y + mâˆ E = 90Â° + 0Â°

= 90Â°

âˆ´âˆ Y and âˆ E are a pair of complementary angles.

iii. mâˆ D + mâˆ F = 75Â° + 15Â°

= 90Â°

âˆ´âˆ D and âˆ F are a pair of complementary angles.

iv. mâˆ B + mâˆ G = 60Â° + 120Â°

= 180Â°

âˆ´âˆ B and âˆ G are a pair of supplementary angles.

v. mâˆ N + mâˆ J = 30Â° + 150Â°

= 180Â°

âˆ´âˆ N and âˆ J are a pair of supplementary angles.

Question 3.

In Î”XYZ, mâˆ Y = 90Â°. What kind of a pair do âˆ X and âˆ Z make?

Solution:

In Î”XYZ,

mâˆ X + mâˆ Y + mâˆ Z = 180Â° â€¦.(Sum of the measure of the angles of a triangle is 180Â°)

âˆ´mâˆ X + 90 + mâˆ Z = 180

âˆ´mâˆ X + 90 + mâˆ Z â€“ 90 = 180 â€“ 90 â€¦.(Subtracting 90 from both sides)

âˆ´mâˆ X + mâˆ Z = 90Â°

âˆ´âˆ X and âˆ Z make a pair of complementary angles.

Question 4.

The difference between the measures of the two angles of a complementary pair is 40Â°. Find the measures of the two angles.

Solution:

Let the measure of one angle be xÂ°.

âˆ´Measure of other angle = (x + 40)Â°

x + (x + 40) = 90 â€¦(Since, the two angles are complementary)

âˆ´ 2x + 40 â€“ 40 = 90 â€“ 40 â€¦.(Subtracting 40 from both sides)

âˆ´2x = 50

âˆ´x =

âˆ´x = 25

âˆ´x + 40 = 25 + 40

= 65

âˆ´The measures of the two angles is 25Â° and 65Â°.

Question 5.

â‚¹PTNM is a rectangle. Write the names of the pairs of supplementary angles.

Solution:

Since, each angle of the rectangle is 90Â°.

âˆ´ Pairs of supplementary angles are:

i. âˆ P and âˆ M

ii. âˆ P and âˆ N

iii. âˆ P and âˆ T

iv. âˆ M and âˆ N

v. âˆ M and âˆ T

vi. âˆ N and âˆ T

Question 6.

If mâˆ A = 70Â°, what is the measure of the supplement of the complement of âˆ A?

Solution:

Let the measure of the complement of âˆ A be xÂ° and the measure of its supplementary angle be yÂ°.

mâˆ A + x = 90Â°

âˆ´70 + x = 90

âˆ´70 + x â€“ 70 = 90 â€“ 70 â€¦.(Subtracting 70 from both sides)

âˆ´x = 20

Since, x and y are supplementary angles.

âˆ´x + y = 180

âˆ´20 + y = 180

âˆ´20 + y â€“ 20 = 180 â€“ 20 â€¦.(Subtracting 20 from both sides)

âˆ´y = 160

âˆ´The measure of supplement of the complement of âˆ A is 160Â°.

Question 7.

If âˆ A and âˆ B are supplementary angles and mâˆ B = (x + 20)Â°, then what would be mâˆ A?

Solution:

Since, âˆ A and âˆ B are supplementary angles.

âˆ´mâˆ A + mâˆ B = 180

âˆ´mâˆ A + x + 20 = 180

âˆ´mâˆ A + x + 20 â€“ 20 = 180 â€“ 20 â€¦.(Subtracting 20 from both sides)

âˆ´mâˆ A + x = 160

âˆ´mâˆ A + x â€“ x = 160 â€“ x â€¦.(Subtracting x from both sides)

âˆ´mâˆ A = (160 â€“ x)Â°

âˆ´The measure of âˆ A is (160 â€“ x)Â°.

**Intext Questions and Activities**

Question 1.

Observe the figure and answer the following questions. (Textbook pg. no. 26)

T is a point on line AB.

- What kind of angle is âˆ ATB?
- What is its measure?

Solution:

- Straight angle
- 180Â°