What is angle | Type of angles
Angle
Two rays starting from a common point form an angle. In ∠ AOB, O is the vertex, OA and OB are the two rays.
−→.
Measure of a angle
The
amount of turning from OA to OB is called the measure of ∠ AOB, written as m∠ AOB. An angle is measured is degrees denoted
by ‘°’.
Types of angles
(i)
Acute angle: An angle whose measure is greater
than 0° but less than 90° is called an acute angle.
Example: 15° ,30° ,60° ,75° ,etc.
∠ AOB = 30° is an acute angle.
(ii) Right angle: An angle whose measure is 90° is
called a right angle.
∠AOB = 90°is a right angle.
∠AOB = 90°is a right angle.
(iii)
Obtuse angle: An angle whose measure is greater
than 90° and less than 180° is called an obtuse angle.
Example: 100°, 110°, 120°, 140°, etc.
∠AOB = 110° is an obtuse angle.
(iv)
Straight angle: When the rays of an angle are
opposite rays forming a straight line, the angle thus formed is a straight
angle and its measure is 180°.
∠AOB= 180° is a straight angle.
(v)
Reflex angle: An angle whose measure is more
than 180° but less than 360° is called a reflex angle.
∠AOB= 220° is a reflex angle.
(vi)
Complete angle: The angle formed by OP and OQ is one complete circle, that is 360°.Such an
angle is called a complete angle.
This complete rotation is divided into 360 equal parts. Each part
measures 1°.
1° = 60 minutes, written as 60’.
1’ = 60 seconds, written as 60”.
Bisector of an angle
A ray AC is called the bisector of ∠BAD, if m∠BAC = m∠DAC.
In this
case ∠BAC =∠DAC = 1/2∠BAD .
Related Angles
(i) Complementary angles: If the sum of the measures
of two angle is 90°, then the two angles are called complementary angles. Here
each angle is the complement of the other. The complement of 30° is 60°and the
complement of 60° is 30°.
(ii) Supplementary angles: If the sum of the measures
of two angle is 180°, then the two angles are called supplementary angles. Here
each angle is the supplement of the other.
The supplementary angle of 120° is 60° and
the supplementary angle of 60° is 120°.
Adjacent angles
If two angles have the same vertex and a
common ray, then the angles are called adjacent angles. ∠BAC and ∠CAD are adjacent angles (i.e
. ∠x and ∠y) as they have a common ray AC, a common vertex A and both
the angle ∠BAC and ∠CAD are on either side of
the common ray AC, a common vertex A and both
the angle ∠BAC and ∠CAD are on either side of
the common ray AC.
Linear Pair of Angle
Two adjacent angles are said to form a
linear pair of angles, if their non-common ray are two opposite rays.
Angle at a point
Vertically opposite angles
Parallel lines
Two lines l and m in a plane are said to be parallel, if they have no point in common and we represent l∥ m
The distance between two parallel lines always remains the same.
Transversal
A straight line which cuts two or more straight
lines at distinct points is called a transversal.
The Angles formed when a transversal cuts two lines
Let AB and CD be two lines, cut by a transversal t. Then,
the following angles are formed.
(i)
Pairs of corresponding angles:
(a) ∠ 1 = ∠5
(b) ∠ 4 = ∠ 8
(c) ∠ 2 = ∠ 6
(d) ∠ 3 = ∠ 7
(ii)
Pair of alternate interior angles:
(a) ∠ 3 = ∠ 5
(b) ∠ 4 = ∠ 6
(iii)
Pair of consecutive interior angles (Co-interior
angle)
(a) ∠4 + ∠5 = 180
(b) ∠ 3 +∠ 6 = 180
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