Solved Examples and Worksheet for Complementary, Supplementary, Vertical and adjacent Angles

Q1If ∠1 = 125°, then what are the measures of the other angles in the figure?

A. 50°, 135° and 50°
B. 65°, 125° and 45°
C. 55°, 125° and 55°
D. none of the above

Solutions
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Step: 1
If the sum of two angles is 180°, then, the angles are called supplementary angles.
Step: 2
From the figure, ∠1 and ∠2, ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1 form supplementary angles.
Step: 3
∠1 + ∠2 = 180°
  [∠1 and ∠2 form supplementary angles.]
Step: 4
125° + ∠2 = 180°
  [Substitute ∠1 = 125°.]
Step: 5
∠2 = 180° - 125° = 55°
  [Subtract 125° on both the sides.]
Step: 6
∠2 + ∠3 = 180°
  [∠2 and ∠3 form supplementary angles.]
Step: 7
55° + ∠3 = 180°
  [Substitute ∠2 = 55°]
Step: 8
∠3 = 180° - 55° = 125°
  [Subtract 55° on both the sides.]
Step: 9
∠3 + ∠4 = 180°
  [∠3 and ∠4 form supplementary angles.]
Step: 10
125° + ∠4 = 180°
  [Substitute ∠3 = 125°.]
Step: 11
∠4 = 180° - 125° = 55°
  [Subtract 125° on both the sides.]
Correct Answer is :   55°, 125° and 55°
Q2m∠AOC = 30° in the figure. What is m∠COB?

A. 120°
B. 160°
C. 150°
D. 140°

Solutions
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Step: 1
Given, ∠AOC = 30°.
Step: 2
Sum of ∠AOC and ∠COB is 180°.
  [AB is a straight line.]
Step: 3
Hence, ∠AOC + ∠COB = 180°.
Step: 4
30° + ∠COB = 180°.
  [Substitute ∠AOC = 30°.]
Step: 5
∠COB = 180° - 30° = 150°
  [Subtract 30° on both sides.]
Correct Answer is :   150°
Q3Choose the pair of angles that are congruent and vertical to each other.


A. ∠3 and ∠4
B. ∠2 and ∠4
C. ∠5 and ∠4
D. ∠5 and ∠8

Solutions
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Step: 1
When two lines intersect, two pairs of congruent opposite angles are formed. angles in each such pair are called vertical angles.
Step: 2
Amongst the choices, ∠2 and ∠4 are the pair of vertical angles.
Correct Answer is :   ∠2 and ∠4
Q4m∠AOC = 25o in the figure. What is m∠COB?

A. 115o
B. 165o
C. 145o
D. 155o

Solutions
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Step: 1
Given, ∠AOC = 25o.
Step: 2
Sum of ∠AOC and ∠COB is 180o.
  [Since, AB is a straight line.]
Step: 3
Hence, ∠AOC + ∠COB = 180o.
Step: 4
25o + ∠COB = 180o.
  [Substitute ∠AOC = 25o.]
Step: 5
∠COB = 180o - 25o = 155o
  [Subtract 25o on both sides.]
Correct Answer is :   155o
Q5Find the measure of the angle x.

A. 130°
B. 120°
C. 60°
D. 50°

Solutions
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Step: 1
When two adjacent angles form 180° they are called supplementary angles.
Step: 2
∠x and 130° are adjacent angles.
Step: 3
∠x + 130° = 180°
  [Sum of supplementary angles = 180°]
Step: 4
∠x = 180° - 130°
Step: 5
∠x = 50°
Step: 6
Therefore, the supplementary angle of 130° is 50°.
Correct Answer is :   50°
Q6In the figure, which two angles are supplementary?


A. l and q
B. None of these
C. l and p
D. m and q

Solutions
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Step: 1
If a transversal intersects two parallel lines, the interior angles are supplementary.
Step: 2
In the figure, l and q are interior angles. Hence, they are supplementary.
Step: 3
So, l and q are supplementary angles.
Correct Answer is :   l and q
Q7Find the measure of ∠M.

A. 45°
B. 70°
C. 80°
D. 90°

Solutions
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Step: 1
In Δ MNO, ∠MON = 180° - 135° = 45°
Step: 2
∠MNO = ∠MON = 45°
Step: 3
∴ ∠M = 180° - (45° + 45°) = 90°
Correct Answer is :   90°

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