PROBLEMS ON ADJACENT ANGLES

Find the unknown values of the following.

Problem 1 :

Solution :

90 + d + 140 = 360

230 + d = 360

Subtracting 230, we get

d = 360 - 230

d = 130

Problem 2 :

Solution :

2g + 3g + 90 = 360

5g + 90 = 360

5g = 360 - 90

5g = 270

g = 270/5

g = 54

Problem 3 :

Solution :

e + e + e = 360

3e = 360

Dividing by 3, we get

e = 360/3

e = 120

Problem 4 :

Solution :

x + 30 + 2x + 15 = 180

3x + 45 = 180

3x = 180 - 45

3x = 135

x = 135/3

x = 45

Problem 5 :

Solution :

2x + 5 + 15x = 90

17x + 5 = 90

Subtracting 5, we get

17x = 90 - 5

17x = 85

Dividing by 17, we get

x = 85/17

x = 5

Problem 6 :

Solution :

3x + 67 + x - 31 + 3x + 30 = 360

7x + 67 + 30 - 31 = 360

7x + 66 = 360

7x = 360 - 66

7x = 294

x = 294/7

x = 42

Problem 7 :

Use the figure shown.

a. Name a pair of adjacent angles.

b. Name a pair of vertical angles.

Solution :

a) ∠ABC and ∠ABF share a common side and have the same vertex B. So, ∠ABC and ∠ABF are adjacent angles.

b) ∠ABF and ∠CBD are opposite angles formed by the intersection of two lines. So, ∠ABF and ∠CBD are vertical angles.

Problem 8 :

Name two pairs of adjacent angles and two pairs of vertical angles in the figure.

Solution :

Adjacent angles will share the common vertex.

• ∠ZWV and ∠VWX are adjacent angles.
• ∠ZWY and ∠YWX are adjacent angles.

Vertical angles should lie opposite.

• ∠ZWV = ∠XWY are vertical angles
• ∠VWX = ∠ZWY are vertical angles  

Problem 9 :

Solution :

Adjacent angles will share the common vertex.

• ∠NJP and ∠PJQ are adjacent angles.
• ∠QJK and ∠KJL are adjacent angles.
• ∠LJM and ∠MJN are adjacent angles.

Vertical angles should lie opposite.

• ∠PJQ = ∠MJL are vertical angles
• ∠NJM = ∠QJK are vertical angles

Problem 10 :

If angles x and y form a linear pair and x – 2y = 30°, then the value of y is

(a) 50°     (b) 110°     (c) 210°    (d) 60°

Solution :

Since x and y are linear pair, the sum of the angles will be equal to 180 degree.

x + y = 180 -----(1)

x - 2y = 30 -----(2)

(1) - (2)

x + y - (x - 2y) = 180 - 30

x + y - x + 2y = 150

3y = 150

y = 150/3

y = 50

Applying the value of y in (1), we get

x + 50 = 180

x = 180 - 50

x = 130

So, option a is correct.

Problem 11 :

In the figure, AB is a straight line, then the value of (a + b) is

(a) 0°     (b) 90°     (c) 180°     (d) 60°

Solution :

Here a and 90 are adjacent angles. b and 90 are adjacent angles

The sum of these angles must be 180 degree. So, a + 90 + b = 180

a + b = 180 - 90

a + b = 90

Problem 12 :

If ∠AOC = 50° then the value of ∠BOD is ________

(a) 50°       (b) 40°     (c) 130°     (d) 25°

Solution :

• ∠BOC and ∠DOA are vertical angles.
• ∠AOC and ∠DOB are vertical angles.

∠AOC = ∠DOB = 50

So, option a is correct.

Problem 13 :

If two parallel lines are intersected by a transversal, then the interior angles on the same side of transversal are

(a) equal      (b) Adjacent       (c) supplementary     (d) complementary

Solution :

In parallel lines and transversal, the interior angles on the same side of transversal will be co-interior angles and they are supplementary.

Problem 14 :

In figure, l || m value of x is _________

(a) 70°      (c) 210°     (b) 35°     (d) 110°

Solution :

70 and x are co-interior angles, and they are supplementary.

70 + x = 180

x = 180 - 70

x = 110

Problem 15 :

Three parallel lines intersect at __________ points

(a) one    (b) two     (c) three     (d) zero

Solution :

Parallel lines will not intersect each other, then there is no point of intersection. Option d is correct.

Problem 16 :

If one angle of a linear pair is acute, then the other angle will be

(a) right angle     (b) obtuse angle      (c) acute angle     (d) straight angle 

Solution :

Linear pairs should be add upto 18, then if one angle is acute other angle must be obtuse.

Problem 17 :

In the given figure, find the value of y

(a) 18°      (b) 10°       (c) 30°         (d) 36°

Solution :

5y + 2y + 3y = 180

10y = 180

y = 180/18

y = 10

So, the value of y is 10.