#### 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

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°
Q2mAOC = 30° in the figure. What is mCOB? A. 120°
B. 160°
C. 150°
D. 140°

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.]
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

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
Q4mAOC = 25o in the figure. What is mCOB? A. 115o
B. 165o
C. 145o
D. 155o

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.]
Q5Find the measure of the angle x. A. 130°
B. 120°
C. 60°
D. 50°

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°.
Q6In the figure, which two angles are supplementary? A. l and q
B. None of these
C. l and p
D. m and q

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°

Step: 1
In Δ MNO, MON = 180° - 135° = 45°
Step: 2
MNO = MON = 45°
Step: 3
M = 180° - (45° + 45°) = 90°