ADDITIONAL QUESTIONS AND ANSWERS
1) Find the measure of the complement of each of the following angles.
i) 45ᵒ
ii) 54ᵒ
iii) 41ᵒ
iv) 62ᵒ
Ans:
i) The given angle is 45ᵒ
Let its compliment be x
x + 45ᵒ = 90ᵒ
x = 90ᵒ – 45ᵒ → x = 45ᵒ
ii) The given angle is 54ᵒ
Let its compliment be x
x + 54ᵒ = 90ᵒ
x = 90ᵒ – 54ᵒ → x = 36ᵒ
iii) The given angle is 41ᵒ
Let its compliment be x
x + 41ᵒ = 90ᵒ
x = 90ᵒ – 41ᵒ → x = 49ᵒ
iv) The given angle is 62ᵒ
Let its compliment be x
x + 62ᵒ → 90ᵒ
x = 90ᵒ – 62ᵒ → x = 28ᵒ
2) If the angles ( 4 x + 4 )ᵒ and ( 6 x – 4 )ᵒ are supplementary angles, find the value of x.
Ans: ( 4 x + 4 )ᵒ + ( 6 x – 4 )ᵒ = 180ᵒ
∵ sum of supplementary angles is 180ᵒ
4 x + 4 + 6 x – 4 = 180ᵒ
10 x = 180ᵒ → x = 180ᵒ/10 → x = 18ᵒ
3) Find the value of x in the given figure:
Ans: ∠AOB + ∠AOC =180ᵒ ——– linear pair
(2 x + 60)ᵒ + (3 x – 40)ᵒ = 180ᵒ
2 x + 60ᵒ + 3x – 40ᵒ = 180ᵒ
5 x + 20ᵒ = 180ᵒ
5 x = 180ᵒ – 20ᵒ
5 x = 160ᵒ → x = 160ᵒ/5 → x = 32ᵒ
4) Find the value of x.
Ans: (6 x – 40)ᵒ + (5 x + 9)ᵒ + (3 x + 15)ᵒ = 180ᵒ —— sum of angles on a straight line
6x – 40ᵒ + 5 x + 9ᵒ + 3 x + 15ᵒ = 180ᵒ
14 x – 16ᵒ = 180ᵒ
14 x = 180ᵒ + 16ᵒ → 14x = 196ᵒ → x = 196ᵒ/14
x = 14
5) The difference in the measures of two complementary angles is 12ᵒ. Find the measure of the angles.
Ans: Let the first angle be x
The second angle = x – 12ᵒ
x + (x – 12) = 90ᵒ ———- sum of complementary is 90ᵒ
x + x – 12 = 90ᵒ
2 x – 12 = 90ᵒ →2 x = 90ᵒ + 12→ 2 x = 102ᵒ
x = 102ᵒ/2 → x = 51ᵒ
6) Which of the following pairs of angles are supplementary:
Ans:
i) 110ᵒ + 50ᵒ = 160ᵒ
∴ The angles are not supplementary as sum of their angles is not 180ᵒ.
ii) 50ᵒ + 130ᵒ = 180ᵒ
∴ The angles are supplementary as their sum is 180ᵒ.
iii) 115ᵒ + 65ᵒ = 180ᵒ
∴ The angles are supplementary as their sum is 180ᵒ.
iv) 45ᵒ + 45ᵒ = 90ᵒ
∴ The angles are not supplementary as their sum of their angles is not 180ᵒ.
7) In the given figure, if ∠1 = 30ᵒ, find ∠2 and ∠3.
Ans: ∠1 + ∠2 = 180ᵒ —— linear pair
30ᵒ + ∠2 = 180ᵒ
∠2 = 180ᵒ – 30ᵒ
∠2 = 150ᵒ
∠1 = ∠3 ——- vertically opposite angles
∠3 = 30ᵒ
8) Name the pairs of angles in each figure:
Ans:
Corresponding angles
Angles on the same side of the transversal
Alternate interior angles
Alternate interior angles
Corresponding angles
Linear pair
9) In the given figure, identify
i) Pairs of corresponding angles
Ans:: ∠1 and ∠8, ∠7 and ∠6
∠5 and ∠4, ∠3 and ∠2
ii) Interior angles on the same side of the transversal
Ans:: ∠5 and ∠6, ∠3 and ∠8
iii) Alternate interior angles
Ans:: ∠3 and ∠6, ∠5 and ∠8
iv) Angles forming linear pair
Ans:: ∠1 and ∠7, ∠3 and ∠5, ∠1 and ∠3, ∠7 and ∠5, ∠8 and ∠6, ∠2 and ∠4, ∠8 and ∠2,
∠6 and ∠4.
v) Alternate exterior angles
Ans:: ∠1 and ∠4, ∠7 and ∠2
10) Find measure of a, b, c, d from the following figure line p // q, m // n
Ans:
a + 60 = 180ᵒ —— angles on the same side of the transversal
a = 180ᵒ – 60ᵒ
∴ a = 120ᵒ
Let us assume ∠t on line q such that
∠a = ∠t ——- corresponding angles
∠t = 120ᵒ
∠t = ∠d ——- vertically opposing angles
∴ ∠d = 120ᵒ
∠d + ∠c = 180ᵒ —— linear pair
120ᵒ + ∠c = 180ᵒ
∠c = 180ᵒ − 120ᵒ
∴ ∠c = 60ᵒ
∠b = ∠c —— vertically opposite angles
∴∠b = 60ᵒ
11) In the given figure p // q. Find the values of x, y, and z.
Ans: ∠z = 120ᵒ —– alternate interior angles
∠y = 40ᵒ —– alternate interior angles
∠x + ∠y + ∠z = 180ᵒ —- sum of angles on a straight line
∠x + 40ᵒ + 120ᵒ = 180ᵒ
∠x + 160ᵒ = 180ᵒ
∠x = 180ᵒ − 160ᵒ
∠x = 20ᵒ
Thus , ∠x = 20ᵒ , ∠y = 40ᵒ , ∠z = 120ᵒ