Pairs of angles are discussed here in this lesson.
1. Complementary Angles:
Two angles whose sum is 90° (that
is, one right angle) are called complementary angles and one is called the complement of the other.
Here, ∠AOB = 40° and ∠BOC = 50°
Therefore, ∠AOB + ∠BOC = 90°
Here, ∠AOB and ∠BOC are called complementary angles.
∠AOB is complement of ∠BOC and ∠BOC is complement of ∠AOB.
For Example:
(i) Angles of measure 60° and 30° are complementary angles because 60° + 30° = 90°
Thus, the complementary angle of 60° is the angle measure 30°. The complementary angle angle of 30° is the angle of measure 60°.
(ii) Complement of 30° is → 90°  30° = 60°
(iii) Complement of 45° is → 90°  45° = 45°
(iv) Complement of 55° is → 90°  55° = 35°
(v) Complement of 75° is → 90°  75° = 15°
Working rule: To find the complementary angle of a given angle subtract the measure of an angle from 90°.
So, the complementary angle = 90°  the given angle.
2. Supplementary Angles:
Two angles whose sum is 180° (that
is, one straight angle) are called supplementary angles and one is called the supplement of the other.
Here, ∠PQR = 50° and ∠RQS = 130°
∠PQR + ∠RQS = 180° Hence, ∠PQR and ∠RQS are called supplementary angles and ∠PQR is
supplement of ∠RQS and ∠RQS is supplement of ∠PQR.
For Example:
(i) Angles of measure 100° and 80° are supplementary angles because 100° + 80° = 180°.
Thus the supplementary angle of 80° is the angle of measure 100°.
(ii) Supplement of  55° is 180°  55° = 125°
(iii) Supplement of 95° is 180°  95° = 85°
(iv) Supplement of 135° is 180°  135° = 45°
(v) Supplement of 150° is 180°  150° = 30°
Working rule: To find the supplementary angle of a given angle, subtract
the measure of angle from 180°.
So, the supplementary angle = 180°  the given angle.
3. Adjacent Angles:
Two non – overlapping angles are said to be adjacent angles if they have:
(a) a common vertex
(b) a common arm
(c) other two arms lying on opposite side of this common arm, so that their interiors do not overlap.
In the above given figure, ∠AOB and ∠BOC are non – overlapping, have OB as the common arm and O as the common vertex. The other arms OC and OA of the angles ∠BOC and ∠AOB are an opposite sides, of the common arm OB.
Hence, the arm ∠AOB and ∠BOC
form a pair of adjacent angles.
4. Vertically Opposite Angles:
Two angles formed by two intersecting lines having no common arm are called vertically opposite angles.
In the above given figure, two lines \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) intersect each other at a point O.
They form four angles ∠AOC, ∠COB, ∠BOD and ∠AOD in which ∠AOC and ∠BOD are vertically opposite angles. ∠COB and ∠AOD are vertically opposite angle.
∠AOC and ∠COB, ∠COB and ∠BOD, ∠BOD and ∠DOA, ∠DOA and ∠AOC are pairs of adjacent angles.
Similarly we can say that, ∠1 and ∠2 form a pair of vertically opposite angles while ∠3 and ∠4 form another pair of vertically opposite angles.
When two lines intersect, then vertically opposite angles are always equal.
∠1 = ∠2
∠3 = ∠4
5. Linear Pair:
Two adjacent angles are said to form a linear pair if their sum is 180°.
These are the pairs of angles in geometry.
`● Angle.
Interior and Exterior of an Angle.
Measuring an Angle by a Protractor.
Construction of Angles by using Compass.
Geometry Practice Test on angles.
5th Grade Geometry Page
5th Grade Math Problems
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